Safe and efficient autonomous lane changing is a key step of connected automated vehicles (CAVs), which can greatly reduce the traffic accident rate and relieve the traffic pressure. Aiming at the requirements of the smoothness and efficiency of the lane-changing trajectory of CAVs, it is necessary to design the lane changing controller to integrate the sensing, decision-making, and control tasks in the driving process. Firstly, based on the vehicle dynamics model, this paper proposes a vehicle lane-changing control strategy based on NNTSMC method (neural network enhanced non-singular fast terminal sliding mode control). The designed lane-changing controller can well realize the designed path tracking, and both lateral position and yaw angle can well track the expected value. This method enables the vehicle to control the front wheel steering angle intelligently, and the lateral acceleration during steering changes in the small scope, which ensures the steering stability of the vehicle. In this study, an improved adaptive RBF neural network with bounded mapping is designed to estimate the upper bound of the total disturbance of the system, which effectively reduces the chattering phenomenon of the control force. The Lyapunov function constructed in this study proves that the designed controller can ensure the stability of the controlled system. Finally, a comparative experiment is performed by the MATLAB/Simulink-CarSim co-simulation. Compared with SMC and TSMC (non-singular fast terminal sliding mode control), the proposed method has a performance improvement of at least 58.0% and 34.1%, respectively. The effectiveness and superiority of the proposed control method were confirmed by the experiments on the co-simulation platform.