A new compressive sensing(CS) sampling and reconstruction model based on spectral sparse representation is put forward in this paper. The spectral sparse dictionary is constructed from training samples to enhance the effect of sparse representation and the total variation restriction of spatial images is also considered to further enhance the precision during the reconstruction. The experiment to reconstruct 200 bands AVIRIS hyperspectral images show that the effect of spectral sparse representation enhances largely compared with traditional DCT dictionary and Haar wavelet dictionary, and the hyperspectral image is reconstructed nearly perfectly at 25% sampling rate and the spatial and spectral precision is higher than existing common methods in the same condition.