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An adaptive predictive multiplicative autoregressive (APMAR) method is proposed for lossless medical image coding. The adaptive predictor is used for improving the prediction accuracy of encoded image blocks in our proposed method. Each block is first adaptively predicted by one of the seven predictors of the JPEG lossless mode and a local mean predictor. It is clear that the prediction accuracy of an adaptive predictor is better than that of a fixed predictor. Then the residual values are processed by the multiplicative autoregressive (MAR) model with Huffman coding. Comparisons with other methods [MAR, space-varying MAR (SMAR) and adaptive JPEG (AJPEG) models] on a series of test images show that our method is suitable for reversible medical image compression.