This paper studies co-prime sampling for two-dimensional synthetic aperture radar (SAR) imaging and proposes a new approach based on co-prime up-sampling and compressive sensing to improve the resolution of SAR images. In order to decrease the redundancy in SAR phase history, we extend the co-prime down sampling structure to the fast-time domain and introduce a random matrix to compress the data in the slow-time domain. Since the SAR image is very sparse, directly applying compressive sensing algorithm can not recover clear picture. As a result, co-prime up-sampling with gradient projection for sparse reconstruction (GPSR) algorithm is proposed in this work. Simulation results show that even after data reduction, the new approach could still acquire high resolution images. The compression ratio could be 10:1 overall.