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Experimental research is essential in the development of a hybrid electric vehicle. In this study, a bench test was conducted for a compound power-split hybrid electric vehicle (PSHEV) to analyze the real dynamic characteristics of its components and the factors of system shock and vibration during the engine start-up process. Firstly, the mode switching process with an engine start-up was divided into four stages by the lever method. The basic control strategy of mode switching with engine start-up was formulated and tested on a bench test platform. Secondly, based on the bench test data, the output characteristics of the battery motor, engine, and driveshaft were analyzed in detail. The main variable parameters of the engine control unit were investigated in the engine start-up process. Ultimately, the results showed that the engine’s pulsating torque was the main reason for system jerk and vibration during the engine start-up process, and the excessive intake manifold pressure before the engine’s ignition was one of the main reasons for the large output torque ripple. When initiating the electric engine starting process, the jerk and vibration presented a wide fluctuation. The maximum value of the equivalent jerk was 92.12 m/s³, and the maximum value of the absolute value of the vibration acceleration was 4.077 m/s².