A fast and accurate synthetic aperture radar raw data generator of moving targets has high importance, especially in the applications of the ground moving target indication. In this paper, by the hybrid time-frequency domain, a fast algorithm has been proposed for strip mode SAR raw data generation of moving targets. Using this simulator, in different conditions in terms of target motion speed, acceleration and direction, radar raw data has been generated and its final image has been extracted by Range-Doppler Algorithm. Then, the obtained images have been studied using the formula that have been extracted for predicting the effects of target motion parameters in the SAR images. The results show that the proposed simulator has a better performance in terms of speed than other existing simulators.