An active control method for the stability of a high-speed train was proposed based on the lateral vibration of the bogie frame. Two implementation schemes, namely the lateral vibration control of the frame by the inertial actuator and the active elastic suspension of the power bogie drive system, were carried out. The vehicle hunting stability index and control force were utilized as two objective functions, and the genetic algorithm (NSGA-II) was used to optimize the control parameters and suspension parameters of the drive system. The results showed that the lateral vibration control of the frame can effectively improve the stability of the bogie, and the time delay of the control system can easily cause system instability, when the direct state feedback of the frame is realized to control the frame vibration. Subsequently, state feedback of additional oscillator was proposed to reduce the influence of time delay. The results showed that reasonable parameters of the additional oscillator can improve the vehicle system stability. A stiffer additional oscillator can increase the critical speed margin of the vehicle system, but it can cause system instability for a certain time delay. Therefore, it is necessary to take into account both the hunting stability of the bogie and the stability of the control system for optimizing the parameters of the additional oscillator. Finally, for the 350 km/h high-speed train bogie, the optimum natural frequency and damping ratio of the additional oscillator were obtained.