The technology of computational spectral imaging changes the traditional imaging modalities by introducing a coded aperture in the optical path to achieve transformation of the targets spectral imformation, then we can get the spectral data cube by reverse transform. This paper introduces the principle of a push-broom imaging coded aperture computational spectral imager. In practical applications, the matching error between the push speed and the frame rate can affect the accuracy of the spectral data reconstruction. The error terms are deduced based on the model of pushroom, the influences of matching errors to the spectral data reconstruction are anlyzed. And the second spectra derivative and strehl ratio are introduced as the evaluation parameters to, respectively, evaluate the reconstructed spectral and spatial image in the data simulation analysis. It showed that, when the accumulated error of a complete set of data is more than one pixel, the shading dramaticly area’s reconstructed results are relatively poor, but the relatively homogeneous regions are affected small; when cumulative error does not exceed half pixel, strehlretio of each channel were above 0.9, and the lower of the spectral energy, the channels strehl ratio smaller, so the more the ranks of the coding template, the higher the platform’s stability required.