Hyperspectral Compressed Sensing (HCS) is crucial for data storage and the real-time transmission of airborne- or spaceborne-based imaging platforms. The Linear Mixing Model (LMM) has been successfully applied to HCS reconstruction. However, the obtained spectrum may be disturbed, thereby limiting the improvement of reconstruction quality due to the influence of illumination conditions, topographic changes, and atmospheric effects. Spectral disturbance is corrected on the basis of LMM by introducing the spectral correction term, and a linear mixing model for spectral perturbation correction is proposed. Moreover, an improved HCS method based on modified LMM is proposed. This proposed model only performs spectral compressed sampling on the original hyperspectral images at the sampling end. The proposed method uses the proposed spectral perturbation correction model to reconstruct the original hyperspectral images based on the compressed sampling data. The alternating direction multiplier method is used to estimate the optimal values of each component in the modified LMM to obtain the optimal reconstruction quality. Experimental results show that the proposed method can achieve better reconstructed performance compared with other classical HCS methods.