This paper presents the development and experimental validation of a novel multi-degrees-of-freedom hand rehabilitation exoskeleton system designed for stroke patients to restore their grasping function. The exoskeleton system includes a two-degrees-of-freedom finger mechanism, an upper computer, and a lower electromechanical subsystem. The fully integrated system makes the exoskeleton more convenient to use and easy to control for grasping assistance with objects used in daily activities. The exoskeleton fingers are powered by a two-degrees-of-freedom driven unit, which allows the exoskeleton to perform movements with a larger range of motion and adequate grasping force. Through four experiments, the exoskeleton system's fingertip force, grasping ability and ability to lift objects were verified.