In order to evaluate the influence of the tracking and imaging platform on the modulation transfer function of the image accurately and provide a theoretical basis for the determination of the platform's technical specifications, an analytical and numerical model is established, which is used to calculate the movement optical transfer function by the image motion function. The truncation error of the finite term is given, and the truncation error is less than 10% when the 7 order approximation is taken. The proposed model includes analytic expressions of low frequency sinusoidal motion and high frequency sinusoidal motion. The tracking angular velocity errors of a tracking imaging platform are analyzed by frequency spectrum. The fundamental components of frequency spectrum are composed by multiple low frequency sinusoidal vibration components. Image motion caused by the tracking angular velocity error can be approximated to uniform linear motion at the exposure time scale. The modulation transfer function is calculated by the statistical moment method, and is almost equal to that calculated by the root mean square of the tracking angular velocity error. The calculated deviation is less than 0.01 at 200 mrad-1frequency. Therefore, the root mean square error of the tracking angular velocity is a reasonable parameter describing the tracking stability of the tracking imaging platform. © 2017, Chinese Lasers Press. All right reserved.