To improve the spatial resolution of hyperspectral image, a super-resolution (SR) method based on GoogLeNet and spatial spectrum transform is proposed. Firstly, the spectral SR framework of remote sensing image is designed to extract different reflection spectra from the image. Then, the coarse pixel spectrum is amplified by using the sparse coding of GoogLeNet, and projected into the high-resolution dictionary to invert the potential SR representation to obtain the super-resolution spectrum. Finally, in order to improve the fidelity of image reconstruction, a coding and decoding structure based on GoogLeNet network is proposed to realize spatial spectral prior transformation. The proposed method is demonstrated experimentally on KSC and other dataset. The results show that the proposed method can effectively reconstruct the image details and texture structure, and the average peak signal-to-noise ratio (APSNR), average structural similarity (ASSIM) and spectral angle mapping (SAM) are better than other comparison methods, and the spectral information is better preserved. Taking KSC data set as an example, APSNR, ASSIM and SAM are 25.643db, 0.789 and 0.084, respectively.