High resolution and wide swath Synthetic Aperture Radar (SAR) imaging increases severely data transmission and storage load. To mitigate this problem, a compressive sensing imaging method is proposed based on wavelet sparse representation of scatter coefficients for stripmap mode SAR. In the presented method, firstly, the signal is sparsely and randomly sampled in the azimuth direction. Secondly, the matched filter is used to perform pulse compression in the range direction. Finally, the wavelet basis is adopted for the sparse basis, and then the azimuth scatter coefficients can be reconstructed by solving the l1 minimization optimization. Even if fewer samples can be obtained in the azimuth direction, the proposed algorithm can produce the unambiguous SAR image. Real SAR data experiments demonstrate that the effectiveness and stability of the proposed algorithm.