Abstract: In order to explore the representation, fast and effective high precision calculation, display and application of mittag-leffler functions, we investigate and implement the four numerical algorithms: the accumulative algorithm, the partitioning algorithm, the optimal parabolic contour algorithm, and the Padé approximation algorithm. Through MATLAB software programming and simulation, the mittag-leffler functions were drawn and displayed, and the performance of four algorithms was analyzed and compared. The experimental results show that the optimal parabolic contour algorithm has the best accuracy and applicability, the Padé approximation algorithm has the fastest calculation speed, and the partitioning algorithm is superior to the accumulative algorithm.