In order to overcome the shortcomings such as low accuracy and high complexity of multi-spectral image demosaicking algorithm in MSFA pattern, a new method of spectral image demosaicking algorithm was proposed based on the advantage of compressed sensing theory in signal reconstruction. Mosaic images were obtained by using a random MSFA pattern. The sampling value of MSFA was equivalent to the data obtained from the perceptual matrix sampling in the compressed sensing theory. The problem of multi-spectral demosaicking of MSFA pattern was transformed into the problem of sparse signal reconstruction in compressed sensing and the spectral correlation of multi-spectral images was utilized. A framework of multi-spectral demosaicking based on compressive sensing was presented. Finally, the optimization method was used to solve the problem of the 0 norm for recovering the multi-spectral image. The objective evaluation results showed that the peak signal to noise ratio of the algorithm was significantly improved compared with those of two algorithms based on Kronecker and the group sparse. Subjective evaluation indicated it could effectively reduce the aliasing in the reconstructed image with better visual effect.