To improve the yaw stability of distributed drive electric vehicles, this paper proposes a yaw stability layered control strategy while considering longitudinal vehicle speed control. For the upper controller, the yaw moment controller is designed based on the sliding mode control principle. Additional yaw moments are obtained by tracking the expected yaw velocity and the sideslip angle respectively, while the total additional yaw moment is obtained by weighted calculation according to vehicle state. The lower controller chooses the tire load rate as the optimization objective function to allocate the torque of each wheel. Finally, a co-simulation model is established by CarSim and Simulink, and two working conditions of double shift line and angular step input are selected for simulation verification. The results demonstrate that the proposed layered control strategy can make the actual yaw velocity and sideslip angle of the vehicle better track the expected value, and effectively enhances vehicle stability.