Supernumerary robotic limbs (SRLs) have been applied in fields of wearable assistance equipment and rehabilitation therapy with good performance and foreground. In view of the shortcomings in the current SRLs design in terms of versatility, dexterity and interactive performance, this paper introduces a dexterous hand mechanism for robotic function conversion and develops a human-robot interactive control system. In addition, to meet the diverse rehabilitation needs of patients, a virtual task environment based on the Unity platform is built, by developing an interactive VR game with active and passive rehabilitation training modes and completing the game architecture design of a customizable hand grasping virtual reality scene combined with the kinematic configuration analysis of dexterous hands. In order to realize its intelligent interactive control, a double-layer feedback control loop based on force and speed has been developed to realize the fine motion control of the dexterous hand, and the output torque adjustment of the dexterous hand is realized by designing the deviation threshold. The results show that the dexterous hand has good interactive performance in hand rehabilitation and human muscle strength enhancement, and the control algorithm has good accuracy and robustness.