Compressive imaging is an important application of the theory of compressive sensing. The deterministic measurements were introduced into compressive imaging and a novel method-compressive double lens imaging was proposed using deterministic phase mask. Simulation results show that novel imaging method can effectively capture the information of image, and reduce the difficulty and costs of the hardware implementation significantly. The classical analog-to-digital conversion of optical imaging is changed, the digital conversion costs are reduced, and the image transmission and storage are able to be facilitated by the proposed method, which provides some theoretical, computing and technical support for new design of camera.