Image interpolation of cross-sections is one of the key steps of medical visualization, and the cubic convolution interpolation is usually employed due to its good tradeoff between computational cost and accuracy, however, sometimes its accuracy can still not meet the requirement. Aimed at the problem, in this paper, the interpolation principle based cubic convolution is firstly analyzed systematically, and then essential relationship among the different cubic convolution interpolation methods is clarified. Lastly,a novel cross-section interpolation method for medical images that is based on the optimal parameter of sharp control is presented. The method takes full advantage of the local characteristic of medical images, and the optimized sharp control parameter is obtained by the iterative computation, and then the cross-section interpolation is performed by the cubic convolution with the optimized parameter in one time. The experimental results show that the method presented in the paper not only can improve the interpolation accuracy effectively, but also is robust.