Rotor dynamic response sensitivity analysis is widely used in rotor model updating， parameter identification and structur? al optimization. In this paper， a first-order， second-order and mixed sensitivity analysis method for dynamic response of rotor sys? tem based on multi-complex domain perturbation method is proposed. The design parameters are perturbed in two complex direc? tions respectively， and the motion equation of the rotor system in the double complex domain is obtained. Using the real matrix ex? pression of the complex number， the complex motion equation is extended to obtain the equivalent real motion equation. By solving the equivalent real motion equation， the system response， first-order sensitivity and second-order sensitivity can be obtained simul? taneously， and the Hessian matrix of dynamic response sensitivity can also be obtained. The numerical simulation analysis of single disk rotor system and gas generator rotor system is carried out to verify the correctness of the rotor dynamic response sensitivity analysis method of multi-complex domain perturbation method. Compared with the traditional finite difference method， the multi complex domain perturbation method shows insensitivity to the error caused by the perturbation step size， and the solution accuracy is higher.