Trajectory tracking is the technology foundation for the autonomous motion control of two-wheeled self-balancing vehicles. Therefore, a dynamical model of a two-wheeled self-balancing vehicle is established using the Lagrangian approach, and a trajectory tracking controller based on the non-singular terminal sliding mode(NTSM) and linear quadratic regulator(LQR) is proposed. Then, a simulation analysis is conducted for the proposed trajectory tracking controller in Matlab/Simulink, and the results show that the vehicle can track the reference trajectory accurately, which validates the effectiveness of the trajectory tracking controller preliminarily. On that basis, combining the inertial measurement unit(IMU) and the ultra wide band(UWB) location technology, the hardware implementation of the controller is presented with the single chip STM32F103C8T6. And the experimental results show that the vehicle can track the reference trajectory well, the horizontal axis deviation is less than 0.2 m, the vertical axis deviation is less than 0.2 m, the steering angle deviation is less than 0.07 rad, and the tilt angle of the vehicle body is less than 0.05 rad except the fluctuation at the start.