Abstract: The nonlinear dynamic model of gear-rotor with random physical and geometrical parameters was established, and many factors were considered, i.e., the gear backlash, the bearing slackness, the time-varying stiffness, the friction between teeth and the static transmission error. In what follows, the nonlinear dynamic equations were transformed into quasi-static governing equations by using the method of Newmark-β step-by-step integration. The mean value and the variance of dynamic displacement response were obtained by exploiting both the algebra synthesis and moment methods which are used for solving the numerical characteristics of random variables. The numerical examples show that the analogical-digital randomness has a rather large effectiveness on the system response, and the impact of the friction coefficient on the vibration amplitude cannot be ignored, especially when the bearing slackness is larger than 10?5m.