Drifting enables the vehicle to quickly adjust its posture and velocity, with the potential to enhance vehicle safety and maneuverability in extreme operating conditions. To improve the handling stability and tracking accuracy of drift control, a controller framework is presented based on model predictive control theory for electronic-two-rear-wheel drive (e-2RWD) automobiles. Primarily, the non-linear bicycle dynamics model is constructed, and in which the motion relationship between the vehicle and the specified trajectory is revealed.Then, a set of reference states are solved for the specified trajectory and desired sideslip. Finally, the MPC drift controller is used to work in conjunction with the wheel speed closed-loop controller to provide coordinated control of the steering angle and both rear wheel drive torques. The performance of the proposed drift controller is assessed in software simulations in two high sideslip driving scenarios with different trajectories. The simulation results show that the proposed controller is able to rapidly enter the steady-state drifting and effectively reduce the fluctuations of vehicle states, striking a reasonable balance between satisficing the accuracy demands and keeping vehicle handling stability. The major contribution of this paper is the first application of the MPC and wheel speed controller combined operation mode to drift control. Due to the advantage of proposed method predicting the vehicle's future dynamic behavior in advance, the controller outputs can be effectively constrained and optimized.