Aiming at the asynchronous motor speed control system with Buck-Boost Matrix Converter (BBMC) as power converter, a frequency conversion speed control method based on finite time control is proposed. Firstly, according to the given speed of the asynchronous motor, the given voltage of the asynchronous motor is obtained by the vector control algorithm based on PI-IP, and the given voltage is used as the reference output voltage of the BBMC. Then the capacitive voltage and inductance current in BBMC are taken as the system control variables, and the duty cycle of the corresponding power switch in BBMC is obtained by the finite time control algorithm, and then the corresponding power in BBMC is opened according to the duty cycle. The output voltage which is consistent with its reference output can be obtained at the output end of BBMC, so that the accurate tracking of the actual speed of asynchronous motor to its given speed can be realized, and the purpose of accurate control of the speed of asynchronous motor can be achieved. Finally, the control method is verified by simulation and experiment. This work is supported by National Natural Science Foundation of China (No. 51477047).