Mode transition is capable of improving the economy of hybrid electric vehicles but may also cause potential crises. When the hybrid power system (hybrid powertrain-HPT) has just completed the mode conversion, the driving system parameters change more dramatically, and the engine torque is fully transferred to the driving motor. Owing to the electromechanical coupling characteristics, HPT may be severely impacted during the operation, causing the instability of initial hybrid drive mode. To solve this problem, the mathematical model of the initial hybrid drive model for a series-parallel hybrid electric vehicle (SPHEV) is constructed. The local stability condition and bifurcation condition were derived to analyse the influence of engine throttle opening, and the instability threshold of the HPT was given. Moreover, an instability control methodology was designed to optimise the operating region of HPT for the initial hybrid drive mode, and vehicle tests of mode transition were carried out based on the existing SPHEV platform. Studies indicate that different throttle opening may lead to changes in bifurcation characteristics, causing the system to exhibit nonlinear behaviour and random oscillations. In addition, the control methodology proposed in this study can improve the stable operating region by 37% and restrain the oscillations of HPT.