Hardmard transfer imaging spectrometer (HTIS) is a novel computationally optical system. Its characteristic of multi-channel multiplexing increases the luminous flux of the optical system without sacrificing spatial resolution, thereby enabling the system’s signal-to-noise ratio to be significantly higher than traditional spectrometer’s. Encoding with digital mirror devices (DMD) in the system causes a serious diffraction effect that gives rise to the apparent degradation of the imaging formation. For improving the image quality and spectral accuracy of the reconstructed data cube, the Hadamard coded spectral imaging data degradation model is established based on the scalar diffraction theory. A data reconstruction algorithm is proposed based on the Lucy Richardson (L-R) algorithm. Through the simulation experiment, the process of image degradation is revealed. On the one hand, it proves that the degradation of system imaging diffraction is the main reason for the distortion of reconstructed data. On the other hand, it verifies the effectiveness of the correction method adopted in this paper. The evaluation result of the spectral angle distance of the restored data cube after L-R correction is 0.1296, and the image similarity evaluation factor is better than 0.85. Compared with the reconstructed data before being corrected, the corrected data is greatly improved in quality. The experimental results show that the algorithm has a good correction effect on the data cube reconstruction of HTIS.