An optimized measurement matrix is designed to compress complex-valued Synthetic Aperture Radar(SAR) images based on Compressive Sensing(CS). The proposed measurement matrix can enhance the incoherence between columns and mitigate the mutual coherence of the measurement matrix effectively giving rise to improvement in the accuracy of reconstruction result. Based on the optimized measurement matrix, a better compression result can be obtained for the complex SAR image. The effectiveness of the proposed method is validated by using the real field data.