Inclusion Criteria:

          1. Signed written Informed Consent.

          2. Age>/= 18 years of age or older.

          3. Histologically confirmed Stage III-IV high-grade epithelial non-mucinous ovarian,
             fallopian tube, or primary peritoneal cancers.

          4. Have received standard of care frontline surgical and chemotherapy treatment (at least
             six cycles of platinum and taxane therapy). Patients who received neoadjuvant therapy
             are included.

          5. Have undergone a second-look surgery by an MD Anderson Gynecologic Oncology faculty
             after having achieved a complete clinical response to frontline surgery and adjuvant
             chemotherapy as evidenced by (a) normal physical exam, (b) normal CT or positron
             emission computed tomography (PET)-CT of abdomen and pelvis or other equivalent
             imaging, and (c) normalization of CA125 (<35 U/mL).

          6. Histologically confirmed residual ovarian cancer at time of second-look surgery.
             Patients with cytological evidence of malignant cells in washings obtained as part of
             the second look procedure are eligible even if biopsies are negative.

          7. Be willing to allow use of archival tissue from second-look surgery and primary
             surgery or biopsy for use in this study.

          8. Have a performance status of 0, 1, or 2 on the Eastern Cooperative Oncology Group
             (ECOG) Performance Scale at the time of screening.

          9. Have adequate organ function as determined by the following laboratory values: a)
             absolute neutrophil count (ANC) >/= 1,000 /mcL; b) Platelets >/= 100,000/mcL; (c) Hgb
             >/= 8 g/dL; (d) Creatinine Clearance >/= 40 mL/min (measured or calculated per local
             practice); (e) Total Bilirubin </= 1.5 × upper limit of normal (ULN) or </= 3 × ULN in
             the case of suspected/documented Gilbert's Syndrome; and (f) AST (SGOT) and ALT (SGPT)
             </= 2.5 X ULN.

         10. Have adequately recovered from second look surgery to be able to start bevacizumab
             within 7 weeks of this procedure.

         11. Negative serum pregnancy within 72 hours prior to receiving the first dose of study
             medication (unless surgically sterile or postmenopausal for greater than one year).

         12. Female subjects of childbearing potential should be willing to use 2 methods of birth
             control or be surgically sterile, or abstain from heterosexual activity for the course
             of the study through 120 days after the last dose of study medication. Subjects of
             childbearing potential are those who have not been surgically sterilized or have not
             been free from menses for > 1 year.

        Exclusion Criteria:

          1. Uncontrolled hypertension as defined by SBP>150 or DBP>90 on at least two separate
             occasions documented in the medical record. Patients would be eligible if blood
             pressure is controlled with appropriate anti-hypertensive therapy. Rescreening after
             this therapy has been instituted is allowed.

          2. Histology showing mucinous or low-grade epithelial ovarian carcinoma.

          3. Planned use of maintenance or consolidative therapy.

          4. History of known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the Study.

          5. History of arterial thrombosis. Patients with history of deep vein thrombosis (DVT)
             are eligible as long as they have received or are receiving appropriate
             anticoagulation therapy.

          6. History of gastrointestinal or urinary fistulae, non-healed or chronic wound, or other
             conditions that, in the investigator's view, would contraindicate or significantly
             increase the risks of bevacizumab therapy.

          7. History of known hemoptysis, gastrointestinal or intracerebral hemorrhage.

          8. Patient that is not able to understand or to comply with the study instructions and
             requirements, or has a history of non-compliance to the medical regimen.

          9. Concurrent or planned use of any other anti-cancer systemic chemotherapy, biological
             therapy (including hormonal or immune therapy), radiation therapy, or live cancer
             vaccines.