Ideal models are usually used in the dynamics analysis of the seeker servo mechanism, and the influences of the random factors such as design tolerance, mismatching tolerance and wear on the system dynamics are seldom taken into account. So it is difficult to describe the actual dynamics correctly. Therefore, the nonlinear dynamics model of the servo mechanism affected by the random excitation is established. The FPK (Fokker - Planck - Kolmogorov) equations of system stochastic dynamics are deduced and solved by the stochastic averaging methods and the points interpolation meshless method synthetically. Then, the random dynamics response is calculated and the influences of the friction on the system random response characteristic are studied. This work can provide theory foundations for evaluating the dynamics of the servo mechanism.