Abstract: A simple and effective reconstruction scheme of hyperspectral data with spectral Compressive Sensing (CS) is proposed based on the widely used linear mixing model. The scheme is different from the traditional reconstruction methods of compressive sensing, which reconstruct hyperspectral data directly. The proposed scheme separates hyperspectral data into endmembers and abundances to reconstruct respectively, then generates hyperspectral data by reconstructed endmembers and abundances. Experimental results show that the reconstruction quality of the proposed scheme is better than the standard compressive sensing, furthermore the computing speed greatly ascends. Simultaneously, as a byproduct, endmembers and abundances can be obtained directly.