Neuroplasticity accompanying learning is a key mediator of stroke rehabilitation. Training in playing music in healthy populations and patients with movement disorders requires resources within motor, sensory, cognitive, and affective systems, and coordination among these systems. We investigated effects of music-supported therapy (MST) in chronic stroke on motor, cognitive, and psychosocial functions compared to conventional physical training (GRASP). Twenty-eight adults with unilateral arm and hand impairment were randomly assigned to MST (n = 14) and GRASP (n = 14) and received 30 h of training over a 10-week period. The assessment was conducted at four time points: before intervention, after 5 weeks, after 10 weeks, and 3 months after training completion. As for two of our three primary outcome measures concerning motor function, all patients slightly improved in Chedoke-McMaster Stroke Assessment hand score, while the time to complete Action Research Arm Test became shorter in the MST group. The third primary outcome measure for well-being, Stroke Impact Scale, was improved for emotion and social communication earlier in MST and coincided with the improved executive function for task switching and music rhythm perception. The results confirmed previous findings and expanded the potential usage of MST for enhancing quality of life in community-dwelling chronic-stage survivors.