Based on double-compressed sampling, a hyperspectral spectral unmixing algorithm is proposed, which could directly complete the endmember extraction and abundance estimation. On the basis of the linear mixed model, we designed spatial and spectral sampling matrices, obtained spatial and spectral measurement data, and constructed a joint unmixing model containing endmember and abundance information. By using operator separation and Lagrangian multiplier algorithm, the endmember matrix, abundance matrix and remixing image can be quickly obtained by matrix operation. The parameters of the unmixing algorithm, including regularization parameter, convergence threshold and spatial sampling rate, are determined using synthetic simulated hyperspectral data. The proposed algorithm is applied to six groups of real hyperspectral data, and the experimental results fully verify the effectiveness and reliability of the algorithm. Compared with the algorithm that directly unmixes the original data, it is found that the proposed algorithm can effectively extract the endmembers and estimate the abundance even when there are few measurement data. Compared with the algorithm of sampling reconstruction first and then unmixing, the proposed algorithm can improve the efficiency of unmixing. Therefore, the main innovation of the proposed algorithm is that it can complete the unmixing directly from the measured data, maintain the accuracy and improve the efficiency of the unmixing.