Model reduction methods for high-dimensional dynamical systems have consistently constituted a significant research topic within the field of nonlinear dynamical systems, significantly influencing the response identification, computation, and prediction of nonlinear vibration systems, soft robots, and complex structural systems. Building upon the invariant manifold reduced method for autonomous self-excited vibration systems by parameterization method and Floquet theory, this paper establishes a parameterization method for reduced model on non-autonomous self-excited vibration systems. By employing a perturbation approximation technique, a parameterization reduced-order model for the forced self-excited system is derived. Using the proposed method, the quasi-periodic solutions and the amplitude-frequency curves varying with external excitation frequency are predicted for a rotor-stator rubbing model incorporating cross-coupled stiffness. The results show that the reduced-order model in this paper can effectively predict the dynamic response of the self-excited vibration system under external force.