A pushbroom spectral imaging system based on compressive sampling was established to realize compressive sensing imaging for a hyperspectral image. An image reconstruction algorithm for this system was investigated. In the image acquisition stage, the pixels of ground imaging line were separated along spectral direction by a prism. Then, the linear encoding between the spectral bands was realized by a digital micro-mirror device. Finally, the encoded spectral bands were summed by a cylindrical lens. In the reconstruction of the compressive sampled data, the traditional compressive sensing reconstruction methods which recover hyperspectral data directly were abandoned. The liner spectral library mixed models were used to convert the reconstructed hyperspectral data into reconstructed abundance fraction matrix, the alternating direction method of multipliers was used to solve the optimizing problem of abundance, and the data was recovered by using the reconstructed abundance and spectral library. The comparison experiment between standard compressive sensing reconstruction and our algorithm shows that the reconstructed average peak signal noise rate of our algorithm is improved about 18 dB than that of the standard compressive sensing when the used data are 20% that of total data. The system is suitable for the spaceborne airborne hyperspectral compressive sensing imaging for its simple sampling.