Inclusion Criteria:

          1. Capable of giving signed informed consent which includes compliance with the
             requirements and restrictions listed in the informed consent form (ICF) and in this
             protocol.

          2. Age ≥19 years at the time of screening

          3. Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 at
             enrollment

          4. Histological or cytological confirmation of advanced NSCLC who progressed following
             platinum-based chemotherapy.

          5. If there is measurable disease based on RECIST 1.1 identified by the investigator at
             screening and there is at least one non-irradiated lesion suitable for selection as a
             target lesion according to RECIST 1.1 on imaging test, tumor assessment by computed
             tomography (CT) scan or magnetic resonance imaging (MRI) must be performed within 28
             days prior to the first dose.

          6. No prior exposure to immune-mediated therapy including, but not limited to, other anti
             CTLA-4, anti-PD-1, anti-PD-L1, and anti programmed cell death ligand 2 (anti-PD-L2)
             antibodies, excluding therapeutic anticancer vaccines for treatment purpose.

          7. In dose escalation phase, 6 DLT evaluable patients whose tumor cell PD-L1 expression
             less than 25% will be enrolled in each cohort. In dose expansion phase, 45 patients
             with confirmed PD-L1-positive NSCLC by using the Ventana SP263 IHC assay will be
             enrolled

               -  Evaluation in newly acquired tumor tissue (preferred) or archival tissue (≤3
                  years old).

               -  If the patient's PD-L1 status has already been assessed using Ventana SP263
                  assay, this test result can be used to assess eligibility for enrollment.

               -  Note: A positive PD-L1 sample is measured using a defined cut-off based on ≥1% of
                  tumor cells with membrane staining of any intensity for PD-L1.

          8. All patients must be able to provide an available tumor sample collected within ≤3
             years after the last anticancer therapies prior to screening. At least 25 patients
             enrolled in the dose expansion phase must be able to provide newly acquired tumor
             biopsy taken within 6 months prior to the first dosing. Tumor lesions used for newly
             acquired biopsies should not be target lesions, unless there are no other lesions
             suitable for biopsy, and only a core needle (not excisional/incisional) biopsy is
             allowed when biopsies are performed on target lesions as there is no other lesions
             suitable for biopsy. In patients with only one target lesion, biopsy for baseline
             tumor evaluation should be performed prior to the imaging test with an interval of at
             least 2 weeks after biopsy. Samples with limited tumor content and fine needle
             aspirate specimens are not acceptable. Specimens from metastatic bone lesions are
             typically unacceptable unless there is a significant soft tissue component. The tumor
             specimen quantity should be as sufficient as possible to allow for exploratory
             biomarker analyses and is preferred in formalin-fixed paraffin embedded blocks. An
             additional subsequent tumour biopsy will be performed on C2D3~6 or C2D10~13 only in
             patients who provide newly acquired tumor biopsy taken within 6 months prior to the
             first dosing. The same tumor lesion should be biopsied at all timepoints, if feasible,
             to avoid introduction of heterogeneity related to the site of tumor or metastasis.

          9. Adequate organ and marrow function as defined below:

               -  Hemoglobin ≥9.0 g/dL

               -  Absolute neutrophil count ≥1.0 × 109 /L

               -  Platelet count ≥75 × 109/L

               -  Serum bilirubin ≤1.5 × the upper limit of normal (ULN). This will not apply to
                  patients with confirmed Gilbert's syndrome, who will be allowed enrollment in
                  consultation with their physician.

               -  ALT and AST ≤2.5 × ULN; for patients with hepatic metastases, ALT and AST ≤5 ×
                  ULN

               -  Measured creatinine clearance (CL) >40 mL/min or Calculated creatinine clearance
                  (CL) >40 mL/min as determined by Cockcroft-Gault (using actual body weight)

         10. Must have a life expectancy of at least 12 weeks

         11. Body weight >30 kg

         12. Male and/or female

        Exclusion Criteria:

          1. History of allogeneic organ transplantation.

          2. Active or prior documented autoimmune or inflammatory disorders (including
             inflammatory bowel disease [e.g., colitis or Crohn's disease], diverticulitis [with
             the exception of diverticulosis], systemic lupus erythematosus, Sarcoidosis syndrome,
             or Wegener syndrome [granulomatosis with polyangiitis, Graves' disease, rheumatoid
             arthritis, hypophysitis, uveitis, etc.]). The following are exceptions to this
             criterion:

               -  Patients with vitiligo or alopecia

               -  Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on
                  hormone replacement

               -  Any chronic skin condition that does not require systemic therapy

               -  Patients without active disease in the last 5 years may be included but only
                  after consultation with the Study Physician

               -  Patients with celiac disease controlled by diet alone

          3. Uncontrolled intercurrent illness, including but not limited to, ongoing or active
             infection, symptomatic congestive heart failure (New York Heart Association [NYHA]
             Class III/IV), uncontrolled hypertension (≥150/90 mmHg), unstable angina pectoris,
             myocardial infarction (≤ 6 months prior to screening), clinically significant cardiac
             valvulopathy requiring treatment, uncontrolled cardiac arrhythmia, interstitial lung
             disease, serious chronic gastrointestinal conditions associated with diarrhea, or
             psychiatric illness/social situations that would limit compliance with study
             requirement, substantially increase risk of incurring AEs or compromise the ability of
             the patient to give written informed consent

          4. History of another primary malignancy except for

               -  Malignancy tumors with low risk of recurrence treated with curative intent and
                  with no known active disease ≥5 years before the first dose of IP Adequately
                  treated non-melanoma skin cancer or lentigo maligna without evidence of disease

               -  Adequately treated carcinoma in situ without evidence of disease

          5. History of leptomeningeal carcinomatosis

          6. History of active primary immunodeficiency

          7. Active infection including tuberculosis (clinical evaluation that includes clinical
             history, physical examination and radiographic findings, and tuberculosis testing in
             line with local practice), hepatitis B (HBV surface antigen [HBsAg] test positive),
             hepatitis C, or human immunodeficiency virus (positive HIV 1/2 antibodies). Patients
             with a past or resolved HBV infection (defined as the presence of hepatitis B core
             antibody (anti-HBc) and negative of HBsAg) are eligible. Patients positive for
             hepatitis C (HCV) antibody are eligible only with negative HCV RNA measured by
             polymerase chain reaction.

          8. Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the
             exception of alopecia, vitiligo, and the laboratory test results coinciding with the
             inclusion criteria

               -  Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after
                  consultation with the Study Physician.

               -  Patients with irreversible toxicity expected not to be exacerbated by study
                  treatment may be included only after consultation with the Study Physician.

          9. In the case of brain metastases or spinal cord compression, patients with suspected
             brain metastases at screening should undergo a brain MRI (preferred) or CT test using
             IV contrast medium prior to study entry. Brain metastases will not be recorded as
             RECIST Target Lesions at baseline. Note: Patients whose brain metastases have been
             treated may participate provided they show radiographic stability defined as 2 brain
             imaging results, both of which are obtained after treatment to the brain metastases.
             These imaging scans should both be obtained at least 4 weeks apart and show no
             evidence of intracranial progression. In addition, any neurologic symptoms that
             developed either as a result of the brain metastases or their treatment must have
             resolved or be stable either, without the use of steroids, or are stable on a steroid
             dose of ≤10 mg/day of prednisone or its equivalent for at least 14 days prior to the
             start of treatment.

         10. QT interval corrected for heart rate using Fridericia's formula (QTcF) ≥450 ms in male
             and ≥470 ms in female

         11. Known allergy or hypersensitivity to any of the study drugs or the study drug
             excipients Prior/concomitant therapy

         12. Administration of the last dose of anticancer therapy (chemotherapy, endocrine
             therapy, targeted therapy, biologic therapy, tumor embolization, or monoclonal
             antibodies) ≤ 3 weeks prior to the first dose of study drug. If sufficient wash-out
             time has not occurred due to the medication administration schedule or PK properties
             of an agent, a longer wash-out period will be required, as agreed by Sponsor and the
             Investigator. Concurrent use of following therapies is acceptable.

               -  Hormonal therapy with gonadotropin-releasing hormone (GnRH) agonists or
                  antagonists for prostate cancer

               -  Hormone-replacement therapy or oral contraceptives

               -  The situation in which a regulatory agency allows a regulatory agency approved
                  tyrosine kinase inhibitor (TKI) is the case in which TKI is administered prior to
                  a period of at least 7 days beginning on day 1 of the first cycle of the
                  trial.Baseline scans must be obtained after discontinuation of prior TKIs, and
                  registration criteria pertaining to adverse events related to prior anticancer
                  therapies must be met.

               -  The situation in which herbal therapy is allowed is when the herbal medicine has
                  been administered at least one week prior to Day 1 of Cycle 1.

         13. Radiotherapy with a limited field of radiation for palliation within 1 week of the
             first dose of study treatment, with the exception of patients receiving radiation to
             more than 30% of the bone marrow or with a wide field of radiation which must be
             completed within 4 weeks of the first dose of study treatment.

         14. Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note:
             Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to
             30 days after the last dose of IP.

         15. Major surgical procedure (as defined by the Investigator) within 28 days prior to the
             first dose of IP. Note: Local surgery of isolated lesions for palliative intent is
             acceptable.

         16. Current or prior use of immunosuppressive medication within 14 days before the first
             dose of study drugs. The following are exceptions to this criterion:

               -  Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra
                  articular injection)

               -  Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of
                  prednisone or its equivalent

               -  Steroids as premedication for hypersensitivity reactions (e.g., CT scan
                  premedication)

         17. The prohibited medications when using vactosertib are following (Refer to Appendix E);

               -  The concurrent use of strong CYP3A4 inhibitors, including but not limited to
                  grapefruit juice, itraconazole, ketoconazole, lopinavir/ritonavir, mibefradil,
                  voriconazole are not allowed in the study (The use of tropical drugs such as 2%
                  ketoconazole cream, may be allowed when discussed with the Sponsor).

               -  The concurrent use of potent CYP3A4 inducers, including but not limited to
                  phenytoin, rifampin, and St. John's wort, are not allowed in the study.

               -  Substances with a sensitive or narrow therapeutic range of CYP including but not
                  limited to: efavirenz, theophylline, darunavir, dasatinib, everylimus, lopinavir,
                  midazolam, sirolimus, ticagrella, astemizole, cisapride, cyclosporine,
                  dihydroergotamine, ergotamine, sirolimus, tacrolimus, terfenadine

               -  Drug use exclusively or mainly removed by UGT1A1 is not allowed in the study.
                  Prior/concurrent clinical study experience

         18. Participation in another clinical study with an investigational product administered
             in the last 30 days

         19. Previous IP assignment in the present study

         20. Concurrent enrollment in another clinical study, excluding an observational (non
             interventional) clinical study or during the follow-up period of an interventional
             study Other exclusions

         21. Female patients who are pregnant or breastfeeding or male or female patients of
             reproductive potential who are not willing to employ effective birth control from
             screening to 90 days after the last dose of durvalumab or vactosertib, whichever is
             longer.

         22. Judgment by the Investigator that the patient should not participate in the study if
             unlikely to comply with study procedures, restrictions, and requirements.

         23. For genetics research study, the followings are excluded;

               -  Previous allogeneic bone marrow transplant

               -  Non-leukocyte-depleted whole blood transfusion within 120 days of genetic sample
                  collection