A dynamical model of the power split powertrain was established to accurately describe the torque and speed coupling relations within the system, aiming at a novel power split hybrid electric vehicle (HEV) with dual planetary gear sets. By means of building the efficiency model of different components, the system operation efficiency under different modes was analyzed. Then, the control framework of the proposed vehicle was designed, and the optimal control problem based on model predictive control scheme was constructed. The one-step Markov chain model was applied to predict the required driver torque and vehicle velocity. The optimal problem in the prediction horizon was converted to nonlinear programming problem, and sequential quadratic programming (SQP) was applied to derive the optimal control sequence. Simulation results demonstrate that the proposed strategy can maintain the battery charging sustainability. When the initial battery state of charge (SOC) is 0.50, 0.55 and 0.60, respectively, compared with the nonlinear predictive control with the engine fuel consumption as objective, the vehicle equivalent fuel economy is improved by 7.17%、5.73% and 10.11%, respectively, with the proposed strategy under urban dynamometer driving schedule (UDDS). Thus, the feasibility and superiority of the controller are validated.