To improve the curve driving stability and safety under critical maneuvers for four-wheel independent drive autonomous electric vehicles, a three-stage direct yaw moment control (DYC) strategy design procedure is proposed in this work. The first stage includes modeling of the tire nonlinear mechanical properties, i.e. the coupling relationship between the tire longitudinal force and the tire lateral force, which is crucial for the DYC strategy design, in the STI (Systems Technologies Inc.) form based on experimental data. On this basis, a 7-DOF vehicle dynamics model is established and the direct yaw moment calculation problem of the four-wheel independent drive autonomous electric vehicle is solved through the nonsingular fast terminal sliding mode (NFTSM) control method. Thus optimal direct yaw moment can be obtained. To achieve this direct yaw moment, an optimal allocation problem of the tire forces is further solved by using the trust-region interior-point method, which can effectively guarantee the solving efficiency of a complex optimization problem such as the tire driving and braking forces allocation of four wheels in this work. Finally, effectiveness of the DYC strategy proposed for autonomous electric vehicles is verified through the CarSim-Simulink co-simulation results.