Aiming at the spatial-spectral correlation characteristics of multispectral images, we propose an end-to-end multispectral image compression method using a convolutional neural network. At the encoding end, multispectral data are fed into the multispectral image compression network, and the main spectral and spatial features of the multispectral image are extracted using convolution. The size of the feature data is reduced by downsampling. The entropy of the spatial-spectral feature data is controlled by the rate distortion, and a dense distribution of spatial-spectral feature data is obtained. The intermediate feature data are quantized and encoded using lossless entropy coding to obtain a compressed bitstream. At the decoding end, the bitstream can be used to reconstruct the multispectral image through an inverse transformation process that involves entropy coding, inverse quantization, upsampling, and deconvolution. Experimental results denote that the proposed method can effectively preserve the spectral information contained in the multispectral images at the same bit rate and improve image reconstruction quality by 2 dB than that of JPEG2000.