In order to make the prosthetic hand complete compliant grasp of different rigid objects, a prosthetic hand control strategy based on fuzzy observation of stiffness is proposed to meet the needs of the speed ratio control in free space and the grip force flexible control in constraint space. Both control process are realized by the same backstepping controller. The expected opening and closing speed, and grip strength are planned by the designed trajectory planner. The conversion from the speed control and the grip force control to the position control is realized. The position backstepping controller is designed and its stability is proved based on Lyapunov stability theory. The designed fuzzy stiffness observer adjusts the parameters of the model in real time, balances the influence of the grasped objects on the control strategy, and switches the control process between free space and constraint space. The control strategy is verified by experiments, and the effectiveness of the control strategy is proved.