Multispectral image compression can considerably reduce the volume of data and promote their application. However, conventional single-scale compression schemes, such as JPEG2000 and three-dimensional set partitioning in hierarchical tree (3D-SPIHT), do not accurately preserve the features of images due to the complex features of multispectral images. A compression framework based on adaptive multiscale feature extraction with a convolutional neural network is proposed. First, an adaptive multiscale feature extraction module, which is the basic component of the compression framework, is designed to extract the multiscale spatial–spectral features of the multispectral images and adaptively adjust the weights of the features according to the content of the images. Second, the encoder, which is composed of multiscale feature extraction modules, extracts the multiscale spatial–spectral features of the multispectral images, and the extracted features are quantized and encoded by the quantizer and the entropy coder to generate a compressed bitstream. Third, the decoder, which is structurally similar to the encoder, is utilized to recover the images. The rate-distortion optimizer is embedded in the encoder to control the trade-off between the rate loss and the distortion. The results of these experiments on multispectral images of the Landsat 8 satellite and the WorldView-3 satellite validate the better performance of our compression framework compared with the performances of conventional schemes, including JPEG2000 and 3D-SPIHT. In order to further verify the effectiveness of multiscale features, the framework is compared with a single-scale compression algorithm based on deep learning, the experimental results validate that the performance of the single-scale compression algorithm superior to the conventional schemes but inferior to our multiscale algorithm, which indicates that the multiscale features can significantly improve the performance of the compression algorithm.