To get a high-ratio compression of remote sensing images, we advanced a new compression method using neural network (NN) and a geometrical multiscale analysis (GMA) tool-ridgelet. Ridgelet is powerful in dealing with linear singularity (or curvilinear singularity with a localized version), so it can represent the edges of images more efficiently. Thus a network for remote sensing image compression is constructed by taking ridgelet as the activation function of hidden layer in a standard three-layer feed-forward NN. Using the characteristics of self-learning, parallel processing, and distributed storage of NN, we get high-ratio compression with satisfying result. Experiment results indicate that the proposed network not only outperforms the classical multilayer perceptron, but also is quite competitive on training of time.