When compressed sensing imaging system is used to imaging, the related motion between the object and imaging system will lead degradation of resolution of the object image. In order to overcome the interference of motion, additional device is employed to acquire the motion parameter of the object, but in many cases the parameter cannot be obtained. Aiming at this problem, it was proposed to use the correlation of object and speckle motion, and apply speckle motion method to offset the object motion interference. Compressed sensing algorithm parameters used multiple groups of different speckle motion parameters to recover the corresponding object image, and at last the correlation criterion parameters was applied to get the object image without motion interference. The influence of the system point spread function was considered in the algorithm, and the deconvolution method was utilized to obtain the object image without the motion and system point spread function influence. Finally, the digital simulation results confirmed the effectiveness of the proposed algorithm.