Asynchronous motor speed control system based on Buck-Boost matrix converter ( BBMC ) has good speed regulation performance. Because the inverter stage of BBMC is a variable structure and nonlinear system, BBMC will produce bifurcation and chaos with the change of parameters, resulting in an unstable state of the system. The main factors affecting the stability of BBMC are the main circuit and control parameters. The control parameters can be continuously optimized in the later stage, and the main circuit parameters cannot be changed once they are determined. This paper studies the stability region of main circuit parameters, and the discrete iterative mapping model of the asynchronous motor speed control system based on BBMC is established. According to the sampling distribution of BBMC output voltage, the influence of main circuit parameters inductance L and capacitance C on the stability of the speed control system is analyzed. The stability region of the main circuit parameters is determined by numerical fitting. Finally, simulation and experiment verify the above analysis’s correctness. The stability region of main circuit parameters can provide the basis for selecting main circuit parameters in practical engineering.