The non-equispaced along-track motion has serious impact on SAR imaging. The SAR images are geometric distorted after the along-track motion compensation, which may impair the quality of the sub-image connection and the multi-spectral SAR image fusion. When the along-track velocity error is large the remained geometric distortion after the interpolation geometric distortion correction can not be ignored. In this paper, a SAR motion compensation algorithm is presented based on Non-Uniform Fast Fourier Transform (NUFFT) directly to the azimuth non-equispaced data. The algorithm has 1 to 2 quantitative reduction in location error and geometric distortion than interpolation geometric distortion correction algorithm and has high robustness on along-track velocity error. At the same time, the amplitude and phase information can both be saved based on the proposed algorithm. The results of the NUFFT compensation for simulated data and the real SAR data verify the effectiveness of the proposed algorithm.