Wavelet transform image compression coding method in the high compression ratio of the reconstructed image quality is often poor. To solve this issue, a coding algorithm based on spectral graph wavelet transform is proposed. In this method, the image is transformed into a graph, the spectral graph wavelet coefficients are obtained by using the spectral graph wavelet transform to decompose the graph, the energy of these coefficients is attenuated with the increase of the scale. Then, the SPECK algorithm is improved according to the characteristics of the spectral graph wavelet coefficients. Finally, the spectral graph wavelet coefficients are quantized, and the quantized coefficients are compressed by the improved SPECK algorithm, and the original image is restored from the sparse coefficients while the amount of image data is compressed. The experimental results show that the coding method is effective for natural image compression, compared with the compression method based on wavelet transform, the PSNR of the reconstructed image is improved and the change is smooth, and has a larger compression ratio at the same time.