Every sub-module of modular multilevel converter contains two IGBTs. With increase the number of system module, the simulation speed is greatly reduced, how to realize the MMC in limited resource becomes the bottleneck of the simulation system of real-time simulation. According to the working principle of IGBT in the sub-module of MMC, the equivalence model of IGBT is two different resistors. Then this paper uses the Thevenin's theorem to build the equivalent mathematic model of sub-module. The correctness of the established sub-module is proved with Matlab/Simulink. Compared with the circuit which uses the device model, the simulation results show that the mathematical model can replace the physical model of MMC sub-module in a certain error range. It has a certain practicality.