The present reversible data hiding algorithms in encrypted medical image have low embedding capacity and need to partition Regions Of Interest (ROI), the receiver operation is not flexible. Combining with the characteristics of medical images, a novel separable reversible data hiding method in encrypted medical images was proposed. Firstly, the medical image with 256 gray levels was decomposed into 8 bit planes, and the highest four bit planes were compressed, which left some space to fill with the peak pixel values. Then the image was reconstructed. The head, middle, tail of the reconstructed image were encrypted respectively. After that, information was embedded in the encrypted image by histogram shifting, and the position was chosen by the data hiding key in the tail. For the receiver, information extraction and image restoration can be separated operations according to keys. The experimental results demonstrate that information can be stored in the compressed image to avoid auxiliary information transmission, which effectively improves the embedding capacity with higher security.