In order to solve the problem of low spatial resolution of hyperspectral image, a method based on spatial spectral joint sparse representation is designed. Firstly, we extract the different reflectance spectra of scenes and obtain a spectral dictionary with strong sparsity and weak coherence by exploiting compressed sensing dictionary learning algorithm. Then using sparsity, non-negativity and spatial structure similarity of hyperspectral image signals, we obtain the sparse coding matrix from the high-spatial resolution low-spectral image of the same scene by the simultaneous orthogonal matching pursuit algorithm. Finally, we combine the spectral dictionary with sparse coding matrix to get the target image. As a result of the combined spatial and spectral information, the simulated data and real data experimental results show that this method can effectively reconstruct image detail information and texture structure compared with bicubic interpolation method and matrix decomposition method, and effectively improve the value of average peak signal-to-noise ratio, average structural similarity, and spectral angel mapper, and maintain the spectral information better.