Abstract The interpolation method of medical image is the key technology in domain of 3-d reconstruction of medical image.In this paper,a new interpolation algorithm based on order morphology is presented.The algorithm is implemented using percent dilation and erosion operations to resolve edge illegibility of the other interpolation algorithms like linear interpolation.The order morphological interpolation technique is compared to an existing shape based interpolation method and its advantages include superiority capability on handling various cases such as the branching and holes problem (appearance and disappearance of information) and more accurate volume estimation.By simulation,the arithmetic is proved an effective method,and the produced slice image is similar to original slice image.