Coded aperture imaging spectrometer is a new type of hyperspectral imaging instrument. The space-borne hyperspectral imager makes images by pushing and sweeping. In the ideal imaging model, it is assumed that one pixel is separated between two adjacent frames so that the target information can be accurately reconstructed. When coding aperture imaging is performed under motion compensation, the moving distance of the object image on the focal plane at each imaging time is different, and there is an amount of dislocation, resulting in decoding error of the decoded and restored data along the direction of the orbit, and the phenomenon of ground object "double shadow" and spectral decoding distortion appear in the simulation image. The amount of misalignment under different compensation modes is different, resulting in different decoding errors. The mathematical model of target data encoding and decoding in push-sweep coded aperture imaging and the mathematical model of field of view optical axis angular velocity in motion compensation mode were constructed. The simulation method of coded aperture imaging hyperspectral data under motion compensation was established, and the simulation data quality was analyzed. Through data quality analysis, it can be seen that under the uniform angular velocity mode, the uniform ground velocity mode and the uniform integral time mode, the cumulative amount of dislocation decreases successively, which is 5.7 m, 0.7 m and 0 m, respectively. The "double shadow" phenomenon of the simulated image becomes less and less obvious, and the image quality becomes clearer and clearer. Meanwhile, the restoration and reconstruction accuracy of the coding aperture imaging improves successively.