In the dynamic process of mode switching of the power-split hybrid electric bus, the vehicle will have longitudinal shock due to the drastic change of the two motors’ torque and the engine’s slow response. To solved this problem, this paper will focus on the process of switching from pure electric mode to hybrid drive mode, considered the operational state changes before and after engine ignition, limited the torque fluctuation transmitted from the front planetary set to the output shaft based on the idea of motor compensation, and calculated the motor compensation torque of the rear planetary set to compensate the torque fluctuation of the output shaft, to reduce the jerk. Firstly, the dynamic models of the transmission system before and after the engine ignition are established, respectively, and then the dynamic torque of the engine is estimated by XGBoost. The estimated value is input into the model predictive controller (MPC) to track the engine speed and calculate the torque fluctuation generated by the front planetary set on the output shaft. Then, according to the estimated value of the engine torque and the predicted value of the engine’s speed, the compensation torque is calculated by the sliding mode controller (SMC). Finally, the vehicle model is built with AVL CRUISE and MATLAB/Simulink software to verify the mode switching control effect of hybrid electric bus under typical urban conditions in China. The results showed that this control strategy significantly reduces the jerk of the mode switching process.