This is a multicenter, randomized, open-label, parallel-group study to compare mLSG15 + KW-0761 to mLSG15 in subjects with CCR4-positive adult T-cell leukemia-lymphoma (untreated primary disease). The primary variable is an efficacy of KW-0761 used as an add-on therapy to mLSG15 as measured in terms of complete response rate (CR/CRu) in the best overall response assessment for antitumor effect. The secondary variables include response rate (CR/CRu/PR) in the best overall response assessment for antitumor effect, complete or response rates by lesion site in the best overall response assessment for antitumor effect, progression-free survival and overall survival. The safety and pharmacokinetic profiles of KW-0761 will be also determined.