For traditional correlated imaging system, the imaging scene is completely sampled by the illumination speckles. According to the compression sensing theory, most of the object information has sparse characteristics under some transformations, and it can be recovered exactly from a relatively small number of samples. A correlated imaging system with sparse speckles is proposed. Imaging scene is illuminated by sparse speckles, and the information of compressed scene is acquired by compressive imaging system. Finally, the complete scene information is accurately restored using compression sensing algorithm. The experimental results show that sparse speckles can effectively reduce the amount of data to improve the imaging efficiency and the quality of the imaging system.