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A compressive imaging method based on motion compensation was proposed to overcome the low-quality problem resulted from the motion of single-pixel imager. Firstly, the compressive sampling model with motion condition was built. Secondly, two image reconstructions, namely, frame-by-frame recovery and joint recovery, were analyzed. Meanwhile? its adaptability to different motion types as well as the distributions of its imaging quality was also discussed. The proposed method makes use of motion information to program the samples instead of reducing integrate time or sampling number, which avoids the decrease of imaging quality. Mathematical simulations and semi-physical experiments show that the proposed method has higher imaging quality than the imaging method without motion compensation. [ABSTRACT FROM AUTHOR]