According to the characteristic of hyperspectral images, a novel iterative hard thresholding (IHT) recovery algorithm based on spectral decorrelation model is proposed. In terms of apparent correlations between the image series, a spectral decorrelation model is established in iterative hard thresholding recovery algorithm. The spectral redundancies are removed in the measured data of current image by the model, and the decorrelation image data is much sparser, which can be reconstructed easily. Experimental results show that the proposed algorithm achieves improved reconstruction performance over IHT algorithms with the same measurement number.