Inclusion Criteria:

          -  Man or woman greater than or equal to (>=) 18 years of age

          -  In Part 1, diagnosis of myelodysplastic syndrome (MDS) according to World Health
             Organization (WHO) criteria

          -  International Prognostic Scoring System (IPSS) low Risk or intermediate-1 risk MDS

          -  Red blood cell (RBC) transfusion dependent, defined as requiring at least 4 RBC units
             transfused over an 8-week period during the 16 weeks prior to Study Entry;
             pre-transfusion hemoglobin (Hb) should be less than or equal to 9.0 gram per deciliter
             (g/dL) to count towards the 4 units total

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0, 1 or 2

        Exclusion Criteria:

          -  Participant has known allergies, hypersensitivity, or intolerance to imetelstat or its
             excipients

          -  Participant has received an investigational drug or used an invasive investigational
             medical device within 30 days prior to Study Entry or is currently enrolled in an
             investigational study

          -  Prior treatment with imetelstat

          -  Have received corticosteroids greater than (>) 30 milligram per day (mg/day)
             prednisone or equivalent, or growth factor treatment within 4 weeks prior to study
             entry

          -  a) Prior treatment with a hypomethylating agent (example [eg], azacitidine,
             decitabine); b) Prior treatment with lenalidomide; c) Has received an
             erythropoiesis-stimulating agent (ESA) or any chemotherapy, immunomodulatory, or
             immunosuppressive therapy within 4 weeks prior to study entry (8 weeks for long-acting
             ESAs)