Path tracking is the rudimentary capability and primary task for autonomous ground vehicles (AGVs). In this paper, a novel four-wheel-independent-steering (4WIS) and four-wheel-independent-drive (4WID) electric vehicle (EV) is proposed which is equipped with steer-by-wire (SBW) system. For path-tracking controller design, the nonlinear vehicle model with 2 degrees of freedom (DOF) is built utilizing the nonlinear Dugoff tire model. The nonlinear dynamic model of SBW system is conducted as well considering the external disturbances. As to the path-tracking controller design, an integrated four-wheel steering (4WS) and direct yaw-moment control (DYC) system is designed based on the model predictive control (MPC) algorithm to track the target path described by desired yaw angle and lateral displacement. Then, the fast terminal sliding mode controller (FTSMC) is proposed for the SBW system to suppress disturbances. The control allocation algorithm of DYC is realized by weighted least square (WLS). To evaluate the performance of the designed controller, numerical simulations of two maneuvers are carried out using a high-fidelity and full-vehicle model via CarSim-Simulink platform. Simulation results show that the integrated 4WS+DYC controller has better path-tracking performance than other controllers, and it has strong robust performance against parametric perturbations, i.e. the road adhesion coefficient and vehicle longitudinal velocity.