Transmission backlash of TV-seeker servo system was an import influence factor for image vibration. In order to analyze the relationship between transmission backlash width and image vibration amplitde, this paper used describing function method to construct nonlinear model of transmission backlash. According to Nyquist stability criterion, the effect of gapsize on the stability of the system was analyzed. And the natural frequency and amplitude of the system were deduced by graphic method. Finally we got the relationship between the TV-seeker's image vibration magnitude and the backlash size. Using Simulink we constructed a whole servo system model to test the effectiveness of the new analysis method.