Hand rehabilitation is critical to the recovery of post-stroke patients. However, designing a modular mechanism of the hand to improve the human-machine compatibility and precision of operation is still a challenge. This paper proposes a new type of hand exoskeleton rehabilitation robot with nine degrees of freedom. With the flexible rods, the passive range of motion for finger adduction/abduction is extended under the premise of independent flexion/extension of the metacarpophalangeal and proximal interphalangeal joint. Based on hand anatomy, the relationship between the offset of the metacarpophalangeal joint and the body height in the process of flexion and extension is discussed, and it is applied to the structure optimization and control system. The genetic algorithm is employed to achieve the size optimization, and the kinematics is analyzed. Finally, a prototype is built and preliminary experiments are carried out, including the range of motion and the grasping ability of the robot. The experimental results show that the robot can realize the patients’ hand rehabilitation function and has certain adaptability.