Abstract: To apply the wave variable method to multi-DOF (degree of freedom) teleoperation system, a more universal wave transform formula suitable for multi-DOF teleoperation system is proposed, and the principle of choosing parameters of the formula is extended. The theory of the wave variable method is analyzed, and the wave transform formula for multi-DOF system is obtained by replacing the wave impedance constant b with wave impedance matrix. From the energy point of view, the selection principle of wave impedance matrix is analyzed, and then the choosing method and the constraint relation of the impedance matrixes are extended based on the selection principle. The passivity of the extended wave impedance matrix is analyzed based on the scattering theory. Taking a 3-DOF master-slave teleoperation system as example, simulation experiments and teleoperation experiments are conducted, and the experimental results show that the proposed wave transform formula can ensure the stability of the multi-DOF teleoperation system with time delays.