Inclusion Criteria:

* Man or woman greater than or equal to (\>=) 18 years of age
* Diagnosis of myelodysplastic syndrome (MDS) according to World Health Organization (WHO) criteria confirmed by bone marrow aspirate and biopsy within 12 weeks prior to Cycle 1 Day 1 (C1D1) (Part 1) or randomization \[Part 2 (Main Study)\]. In Part 2 (Ventricular Repolarization Substudy), diagnosis of MDS or myelodysplastic/myeloproliferative neoplasm with ring sideroblasts and thrombocytosis (MDS/MPN-RS-T) according to WHO criteria confirmed by bone marrow aspirate and biopsy within 12 weeks prior to C1D1
* 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
* 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)
* Part 2 (Main Study): a) Prior treatment with a hypomethylating agent (example \[eg\], azacitidine, decitabine); b) Prior treatment with lenalidomide

Additional Exclusion Criteria for Part 2 (Ventricular Repolarization Substudy)

* Concurrent therapy with medications known to prolong the QT interval and have been associated with Torsade de pointes arrhythmia (TdP)
* Cardiac function abnormalities on screening ECG as follows:

* Resting heart rate outside of 50 to 100 beats per minute
* QTcF \>470 millisecond (msec) (or QTcF \>490 msec in the presence of a right bundle branch block or ventricular conduction delay \[QRS \>119 msec\]), determined by central assessment based on the average value of a triplicate set of ECGs
* Diagnosed or suspected congenital long QT syndrome
* Family history of sudden unexpected death from cardiac-related causes if indicative of a pathogenic mutation of cardiac ion channels
* Family history of congenital long QT syndrome
* History of Mobitz II second degree or third degree heart block
* Implantable pacemaker or automatic implantable cardioverter defibrillator
* Complete left bundle branch block
* Chronic or persistent atrial arrhythmia including atrial fibrillation and atrial flutter
* History or presence of clinically relevant heart rhythm disturbances including atrial, junctional, re-entry, and ventricular tachycardia
* Unusual T-wave morphology (i.e., bifid T-wave) likely to interfere with QT measurements
* History or evidence for any of the following: severe or unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (example, pulmonary embolism, cerebrovascular accident including transient ischemic attacks) within 12 months prior to Cycle 1 Day 1, New York Heart Association (NYHA) Class II to IV heart disease
* Presence of uncontrolled hypertension (persistent systolic blood pressure \[BP\] ≥160 mmHg or diastolic BP ≥100 mmHg). Participants with a history of hypertension are permitted, provided that BP is controlled to within these limits by anti-hypertensive treatment
* Any skin condition likely to interfere with electrocardiographic electrode placement or adhesion
* History of thoracic surgery likely to cause abnormality of the electrical conduction through thoracic tissues