Aiming at the transient overshoot, slow tracking response, and poor steady-state tracking accuracy during the dynamic contact between the robot and the physical environment, a robot impedance control strategy based on fractional order was proposed. First of all, the current method of integer-order impedance control contact process was analyzed, which only relies on changing the update rate and in-decreasing elastic items to adapt to different tasks. A more flexible fractional-order impedance control was designed. According to the inherent properties of fractional impedance, the gain coefficient was designed to map fractional impedance to integer order impedance to facilitate calculation and practical application, and some characteristics of improving integer order impedance control were introduced into fractional impedance to further improve the performance. The dynamically adjustable boundary was analyzed. The simulation results show that the fractional impedance proposed in this paper can directly reduce the contact force overshoot peak generated during the contact process, and has a certain inhibitory effect on the unstable oscillation behaviour of the system. It shows that the fractional impedance is suitable for the application of the contact interaction between robot and dynamic unknown environment.