In this paper, we present a direct solution method based neural network for image compression. The proposed technique includes steps to break down large images into smaller windows and eliminate redundant information. Furthermore, the technique employs a neural network that is trained by a non-iterative, direct solution method. An error backpropagation algorithm is also used to train the neural network, and both training algorithms are compared. The proposed technique has been implemented in C on the SP2 Supercomputer. A number of experiments have been conducted. The results obtained, such as compression ratio and transfer time of the compressed images are presented in this paper.