In this paper, a block-based inter-band predictor (BIP) with multilayer propagation neural network model (MLPNN) is presented by a completely new framework. This predictor can combine with diversity entropy coding methods. Hyperspectral (HS) images are composed by a series high similarity spectral bands. Our assumption is to use trained MLPNN predict the succeeding bands based on current band information. The purpose is to explore whether BIP-MLPNN can provide better image predictive results with high efficiency. The algorithm also changed from the traditional compression methods encoding images pixel by pixel, the compression process only encodes the weights and the biases vectors of BIP-MLPNN which require few bits to transfer. The decoder will reconstruct a band by using the same structure of the network at the encoder side. The BIP-MLPNN decoder does not need to be trained as the weights and biases have already been transmitted. We can easily reconstruct the succeeding bands by using the BIP-MLPNN decoder. The experimental results indicate that BIP-MLPNN predictor outperforms the CCSDS-123 HS image coding standard. Due to a good approximation of the target band, the proposed method outperforms the CCSDS-123 by more than 2.0dB PSNR image quality in the predicted bands. Moreover, the proposed method provides high quality image e.g., 30 to 40dB PSNR at very low bit rate (less than 0.1 bpppb) and outperforms the existing methods e.g., JPEG, 3DSPECK, 3DSPIHT and in terms of rate-distortion performance.