Abstract: Based on the generalized random factor method, the time-variable natural frequencies were analyzed for the torsional vibration of a gear-rotor system with random physical and geometrical parameters. Its stiffness matrix and mass matrix were discomposed into a sum of matrices with same random factors, respectively. Based on the Rayleigh quotient formula, the natural frequencies of the system were changed into a sum of partial ones. And then the mathematic characteristics expressions of the natural frequencies were obtained by utilizing the algebra synthesis method. Finally, an example showed the influence of the randomness of the physical and geometrical parameters on the natural frequencies, and verified the feasibility of the proposed method.