In order to calculate the cooperating characteristic of engine and hydrodynamic torque converter stably and accurately, obtain the best matching of hydrodynamic machine, based on the best matching principles of dynamic and economy, a kind of numerical computational method was put forward. Accuracy of intersection point calculation could be controlled by set step size of torque and rotational speed. The problem of multiple roots and instability of intersection point calculation could be avoided. Based on the graphical user interface (GUI) of MATLAB, the program was completed for matching and the graphs were plotted automatically. By this method, any hydrodynamic torque converter and engine with given performance, input and output cooperating characteristic could be derived accurately, rapidly and stably.