Lossless image coding is important for medical image compression because any information loss or error caused by the image compression process could affect clinical diagnostic decisions. This paper proposes a lossless compression algorithm for application to medical images that have high spatial correlation. The proposed image compression algorithm uses a multi-level decomposition scheme in conjunction with prediction and classification. In this algorithm, an image is divided into four subimages by subsampling. One subimage is used as a reference to predict the other three subimages. The prediction errors of the three subimages are classified into two or three groups by the characteristics of the reference subimage, and the classified prediction errors are encoded by entropy coding with corresponding code words. These subsampling and classified entropy coding procedures are repeated on the reference subimage in each level, and the reference subimage in the last repetition is encoded by conventional differential pulse code modulation and entropy coding. To verify this proposed algorithm, it was applied to several chest radiographs and computed tomography and magnetic resonance images, and the results were compared with those from well-known lossless compression algorithms.