We present an algorithm to achieve good compression and classification for images using vector quantization and a two dimensional hidden Markov model. The feature vectors of image blocks are assumed to be generated by a two dimensional hidden Markov model. We first estimate the parameters of the model, then design a vector quantizer to minimize a weighted sum of compression distortion and classification risk, the latter being defined as the negative of the maximum log likelihood of states and feature vectors. The algorithm is tested on both synthetic data and real image data. The extension to joint progressive compression and classification is discussed.