Two problems exist in which synthetic aperture radar imaging (SAR) for ground -moving targets or ships with strong scattering within high speed platform: one is that the incompatibility between the traditional uniform velocity model in SAR and the high-dynamic characteristic of high speed platform, the other is that defocusing image results in the unpredictability of motion of moving target. Firstly, frequency filtering algorithm used in uniform acceleration model is introduced, an accurate mapping function and an approximately inverse mapping function used in projection is proposed. Then a method of motion compensation based on inertial integrated navigation system(INS) is proposed, which is applied to the acceleration model. At last, PGA autofocus algorithm is adopted to focus the blurring image in Doppler domain. As a result, ground distance map with the target as the center of the image is obtained.