The optical compressive spectral imaging method reconstructs the spectral data cube of the shooting scenery from acquired compressive image data, which has the features such as reducing acquisition data amount, realizing snapshot imaging for certain field of view, increasing signal-to-noise ratio and so on. Due to the mechanism restriction of compressive imaging, the reconstructed spectral data from the single compressive image suffer from fidelity attenuation, which leads to the decrease of the image quality and application ability. Based on the compressive sensing theory, the spatial coding optical compressive spectral imaging system model is developed and multi-frame shooting under variable spatial light modulation conditions is carried out so that high-fidelity cubic data is reconstructed from a certain number of compressive images with the support of optimization method. The AVIRIS imaging data is used to simulate the scenery so that the multi-frame spatial coding optical compressive spectral imaging simulation is carried out and the whole-spectral-region root-mean-square-error is adopted to evaluate the data fidelity quantitatively. The experimental results indicate that with the multi-frame shooting method the data fidelity improves, the imaging quality increases and the spectral curve deviation drops.