According to the strong correlation between the spectrum on hyperspectral images, a method of hyperspectral image compressed sensing is proposed which is based on the linear filter between bands. In terms of apparent correlations between the image series, linear filter between bands is used between reconstruction frame and fomer reconstruction image, to reduce noise information, correct contour information on reconstruction image, and improve the precision of the reconstruction. In the linear filter between bands, low-frequency coefficients of the reconstruction frame are reserved, and high frequency coefficients are summed with the high wavelet transform coefficients of the previous spectrum reconstruction image. Experiment results show that the proposed method can improve the precision of the reconstruction and reduce the reconstruction time.