In order to achieve the secure, efficient storage and transmission of medical images, we propose a joint lossless compression and encryption (JLCE) scheme. First, according to the intra-block correlation degree, the original medical image is divided into two non-overlapping regions with strong correlation and weak correlation. Then, a linear prediction method is performed on the strong correlation region to generate prediction errors; while the integer discrete Tchebichef transform (iDTT) with the properties of energy compaction and perfect image reconstruction is exploited to compact the energy of the weak correlation region and produce the transformed coefficients. Finally, a secure arithmetic encoding algorithm is presented to encode the prediction errors and transformed coefficients and output the encrypted and compressed bitstream. Without secret keys, the outputted encoded result can be decoded by our scheme, but the decoded result doesn’t disclose the content of the original medical image. Experimental results show that, the proposed scheme has satisfactory format compatibility and security and also achieves better performances of compression ratio and computational efficiency compared with some state-of-the-art schemes.