Background Current guidelines for rehabilitation of arm and hand function after stroke recommend that motor training focus on realistic tasks that require reaching and manipulation and engage the patient intensively, actively, and adaptively. Here, we investigated the feasibility of a novel robotic task-practice system, ADAPT, designed in accordance with such guidelines. At each trial, ADAPT selects a functional task according to a training schedule and with difficulty based on previous performance. Once the task is selected, the robot picks up and presents the corresponding tool, simulates the dynamics of the tasks, and the patient interacts with the tool to perform the task. Methods Five participants with chronic stroke with mild to moderate impairments (> 9 months post-stroke; Fugl-Meyer arm score 49.2 ± 5.6) practiced four functional tasks (selected out of six in a pre-test) with ADAPT for about one and half hour and 144 trials in a pseudo-random schedule of 3-trial blocks per task. Results No adverse events occurred and ADAPT successfully presented the six functional tasks without human intervention for a total of 900 trials. Qualitative analysis of trajectories showed that ADAPT simulated the desired task dynamics adequately, and participants reported good, although not excellent, task fidelity. During training, the adaptive difficulty algorithm progressively increased task difficulty leading towards an optimal challenge point based on performance; difficulty was then continuously adjusted to keep performance around the challenge point. Furthermore, the time to complete all trained tasks decreased significantly from pretest to one-hour post-test. Finally, post-training questionnaires demonstrated positive patient acceptance of ADAPT. Conclusions ADAPT successfully provided adaptive progressive training for multiple functional tasks based on participant's performance. Our encouraging results establish the feasibility of ADAPT; its efficacy will next be tested in a clinical trial.