It has been clinically proven that exoskeletons are effective self-training rehabilitation or daily living assistance devices for patients with hand dysfunctions. However, exoskeleton-assisted hand exercises with high degrees-of-freedom are considered as challenging tasks because the digit space, especially the thumb, cannot accommodate enough actuators. In this article, we report a tendon-driven soft hand exoskeleton with a hybrid configuration for thumb actuation. The soft hand exoskeleton system uses the least number of actuators to realize full degrees-of-freedom actuation for all digits. It is tested on a stroke patient with hemiplegia and a healthy subject. The experimental results show that the hand exoskeleton could assist the stroke patient to accomplish various training tasks, such as thumb encircling, grasping, pinching, releasing, and writing. It was found that digit trajectories and joint angle changes of the stroke patient were close to those of the healthy subject. Especially, the range of motion of the stroke patient shows significant improvement with the hand exoskeleton assistance compared to that without the hand exoskeleton assistance. The research in this article paves the way to develop fully actuated soft hand exoskeleton that can be eventually integrated with an electroencephalogram or electromyography for self-training rehabilitation or daily living assistance.