According to an electrical vehicle (EV) construction and working principle, a dynamic model governing its motion was established. A built-in permanent magnet synchronous motor was selected as its driving motor and a mathematical model about the motor working principle was described also. To get good motion effect, a motor driving control system with a current loop and a speed loop was developed. The current loop consists of maximum torque per ampere control and field weakening control. The speed loop is based on a sliding mode control. To make the EV working more smooth, stable and safer, its traction control includes driving motor control and wheel braking control. During some acceleration or cornering, wheel braking control is introduced to keep driving wheels in good slip states, especially to make the car in a good stable and safe state. Simulation study based on MATLAB/Simulink showed the control strategy developed here can make the EV work well, even when it runs on some asymmetric road.