Accurate analysis of cooperating input and output performance of engine and torque converter is the essential of matching hydrodynamic transmission vehicle power system. Accurate calculation of cooperating point is the difficulty and key of cooperating input and output performance analysis of engine and torque converter. Least square higher order polynomial fit was adopted for engine net torque performance curve to get a precise result. At the same time, N equal division method, Newton's method and direct extraction of root were applied respectively to calculate the cooperating point of engine and torque converter. Matlab program language was used and three methods were testified by practical calculation and analysis. The calculating results show that three methods are all effective for the calculation of cooperating point of engine and torque converter.