Abstract: Intelligent electric vehicle longitudinal motion energy optimization can save energy and improve vehicle performance. In order to accurately obtain the energy consumption of the vehicle, the energy consumption optimization problem of the longitudinal motion was solved based on Radau pseudo-spectral method. The longitudinal motion model and energy consumption model was established. Combined with the boundary constraints and path constraints, energy consumption optimization optimal control problem was found. The longitudinal optimum speed trajectory was obtained by solving the problem of minimum energy consumption. This trajectory was used as the desired speed input, the speed tracking control was achieved based on the model predictive control (MPC) algorithm. The experimental results show that, a pure electric vehicles as an example, the policy in this paper can get continuous power consumption value of vehicles traveling, the longitudinal motion with energy-optimized can reduce energy consumption, and the effectiveness of the strategy is verified.