Abstract.To reduce the amount of measurements, compressive sensing (CS) has been introduced to synthetic aperture radar (SAR). In this paper a novel synthetic aperture radar (SAR) imaging algorithm based on compressive sensing (CS) is proposed. In the range plane, the echo signal is reconstructed in fractional Fourier domain for the sparsity, and matched filtering is used in the azimuth to obtain the image. Taking into account the large peak signal to noise ratio (PSNR), raising compression ratio can enhance the resolution, improve the range ambiguity and possess benign focusing ability. Simulation results show that by using the method this paper proposed it outperforms the existing Range Doppler algorithm demonstrating the superior performance of the proposed approach.