Here we propose a novel method to compress the hyperspectral images without loss of any information. Here we use the minimum Descriptor length Adaptive Entropy Predictor. It divides the process of lossless compression of hyperspectral images into three stages: clustering, prediction, and coding. The difference between the predicted and original values is entropy coded using an adaptive range coder for each cluster. In preprocessing Spectral band separation will be done. Integer wavelet transform will be applied to an image. The integer wavelet transform will the integer to integer values. Integer wavelet transform is used to decompose the image. After transformation we will apply minimum description Length Adaptive Entropy Predictor. It will provide encoded image. Encoded image will be given to Inverse Minimum description length Adaptive entropy predictor. It will decode the image. Then we apply the inverse Integer wavelet transform. Finally we get the reconstructed image.