When the sampling ratio and signal- to- noise ratio (SNR) is low, the noise of multispectral image increases, quality of the reconstructed images inevitably degrades. In order to improve the quality of multispectral image, a new prior image constrains hyperspectral compressed sensing (PICHCS) method is proposed. The spatial and spectral correlations in hyperspectral imaging is exploited in PICHCS to reconstruct the primitive images. Prior images obtained by averaging the adjacent spectral primitive images are used as constraints for the compressed sensing image reconstruction. By subtracting each target image with the corresponding prior image, the obtained difference images are expected to sparse and reconstructing the difference images, some of the high SNR characteristics of the prior image are retained in the reconstructions. The feasibility of the method is verified by numerical simulations and experiments. Comparative studies are made for reconstructions obtained with the total variation and low rank joint algorithm and those with PICHCS under different sampling ratios and SNRs. The results indicate that PICHCS improve reconstruction quality of hyperspectral images from a low sampling ratio or SNR dataset, which can reduce the requirement of sampling ratios and the system SNR.