Rehabilitation training for patients with motor disabilities usually requires specialized devices in rehabilitation centers. Home-based multi-purpose training would significantly increase treatment accessibility and reduce medical costs. While it is unlikely to equip a set of rehabilitation robots at home, we investigate the feasibility to use the general-purpose collaborative robot for rehabilitation therapies. In this work, we developed a new system for multi-purpose upper-limb rehabilitation training using a generic robot arm with human motor feedback and preference. We integrated surface electromyography, force/torque sensors, RGB-D cameras, and robot controllers with the Robot Operating System to enable sensing, communication, and control of the system. Imitation learning methods were adopted to imitate expert-provided training trajectories which could adapt to subject capabilities to facilitate in-home training. Our rehabilitation system is able to perform gross motor function and fine motor skill training with a gripper-based end-effector. We simulated system control in Gazebo and training effects (muscle activation level) in Open-Sim and evaluated its real performance with human subjects. For all the subjects enrolled, our system achieved better training outcomes compared to specialist-assisted rehabilitation under the same conditions. Our work demonstrates the potential of utilizing collaborative robots for in-home motor rehabilitation training.Clinical relevance-The collaborative robot system is capable of providing safe and effective training comparable to specialized rehabilitation robots, enabling possibilities of convenient rehabilitation training at home.