Accurately predicting the changes in the speed has a significant impact on the quality of the energy management in hybrid vehicles. Many methods for predicting the speed have been proposed in the literature, but few fully consider vehicle dynamics to predict speed changes. To this end, a new method is introduced to predict the vehicle speed and to perform energy management for hybrid vehicles in situations where lateral dynamics plays a significant role. Based on the tire-road friction coefficient and the GPS signal, the maximum cornering speed of the vehicle, in which each tire force does not saturate, is evaluated. Then, the principle of using less friction braking and using more regenerative braking, the vehicle speed prediction controller is designed. In the end, an optimal control method with a new equivalent factor (EF) adaptive algorithm is designed to distribute the torque of the engine and the motor, as well as the shift schedule of the gearbox. A driver-in-the-loop experiment is used to prove that the vehicle installed with the proposed speed prediction controller has an average 29.1% increase in energy efficiency compared to vehicle that do not have speed prediction controller. And, the EF adaptive algorithm keeps the battery SoC at a reasonable interval.