Background: Cutaneous T-cell lymphomas are rare non-Hodgkin lymphomas with substantial morbidity and mortality in advanced disease stages. We compared the efficacy of mogamulizumab, a novel monoclonal antibody directed against C-C chemokine receptor 4, with vorinostat in patients with previously treated cutaneous T-cell lymphoma. Methods: In this open-label, international, phase 3, randomised controlled trial, we recruited patients with relapsed or refractory mycosis fungoides or Sézary syndrome at 61 medical centres in the USA, Denmark, France, Italy, Germany, the Netherlands, Spain, Switzerland, the UK, Japan, and Australia. Eligible patients were aged at least 18 years (in Japan, ≥20 years), had failed (for progression or toxicity as assessed by the principal investigator) at least one previous systemic therapy, and had an Eastern Cooperative Oncology Group performance score of 1 or less and adequate haematological, hepatic, and renal function. Patients were randomly assigned (1:1) using an interactive voice web response system to mogamulizumab (1·0 mg/kg intravenously on a weekly basis for the first 28-day cycle, then on days 1 and 15 of subsequent cycles) or vorinostat (400 mg daily). Stratification was by cutaneous T-cell lymphoma subtype (mycosis fungoides vs Sézary syndrome) and disease stage (IB–II vs III–IV). Since this study was open label, patients and investigators were not masked to treatment assignment. The primary endpoint was progression-free survival by investigator assessment in the intention-to-treat population. Patients who received one or more doses of study drug were included in the safety analyses. This study is ongoing, and enrolment is complete. This trial was registered with ClinicalTrials.gov, number NCT01728805. Findings: Between Dec 12, 2012, and Jan 29, 2016, 372 eligible patients were randomly assigned to receive mogamulizumab (n=186) or vorinostat (n=186), comprising the intention-to-treat population. Two patients randomly assigned to mogamulizumab withdrew consent before receiving study treatment; thus, 370 patients were included in the safety population. Mogamulizumab therapy resulted in superior investigator-assessed progression-free survival compared with vorinostat therapy (median 7·7 months [95% CI 5·7–10·3] in the mogamulizumab group vs 3·1 months [2·9–4·1] in the vorinostat group; hazard ratio 0·53, 95% CI 0·41–0·69; stratified log-rank p<0·0001). Grade 3–4 adverse events of any cause were reported in 75 (41%) of 184 patients in the mogamulizumab group and 76 (41%) of 186 patients in the vorinostat group. The most common serious adverse events of any cause were pyrexia in eight (4%) patients and cellulitis in five (3%) patients in the mogamulizumab group; and cellulitis in six (3%) patients, pulmonary embolism in six (3%) patients, and sepsis in five (3%) patients in the vorinostat group. Two (67%) of three on-treatment deaths with mogamulizumab (due to sepsis and polymyositis) and three (33%) of nine on-treatment deaths with vorinostat (two due to pulmonary embolism and one due to bronchopneumonia) were considered treatment-related. Interpretation: Mogamulizumab significantly prolonged progression-free survival compared with vorinostat, and could provide a new, effective treatment for patients with mycosis fungoides and, importantly, for Sézary syndrome, a subtype that represents a major therapeutic challenge in cutaneous T-cell lymphoma. Funding: Kyowa Kirin.