A novel dual-motor coupling powertrain (DMCP) with speed and torque coupling is proposed. In this powertrain, a planetary gear unit couples the speed of two motors, and another shaft-fixed gear unit couples the torque of two motors. By means of integrated control, the electric motors, synchronizer, and clutches, the DMCP can operate in four modes to satisfy the demands of different running conditions, thereby improving the energy utilization efficiency. In this paper, the operating principles of the DMCP in various modes are analyzed, and the instantaneous overall efficiency is optimized based on the vehicle longitudinal kinetic theory. Moreover, this paper formulates the optimal mode shift strategy and the power split strategy of the DMCP, and a detailed dual-motor electric vehicle (EV) model is developed in the MATLAB/Simulink environment. The simulation result indicates that, compared with the normal single-motor two-speed powertrain, the DMCP can effectively improve the energy utilization efficiency of the EV and extends the EV's driving range.