The working environment of heavy-duty special vehicles is complex, so during operation and driving, high demands are placed on the vehicle’s steering performance. To improve both the motility of low-speed steering and stability of high-speed steering of five-axis heavy-duty special vehicle, a full-wheel active steering control method is proposed according to the genetic algorithm optimized linear quadratic regulator (GA-LQR). The LQR is designed considering the cost of vehicle state error and the increment of wheel angle input. The vehicle monorail model is established and simulation is conducted at 15 and 60 km/h in Matlab/Simulink environment. The numerical results show that the designed control system enables the vehicle to have a minimum turning radius of 7.9 m comparing to that of 8.4 m from the uncontrolled model at low speeds and can also balance the handling stability and driver’s driving experience at high speeds. Furthermore, compared to the LQR based controller, it can significantly reduce the maximum values of sideslip angle by 83% at low speeds and 97% at high speeds, as well as the time to reach steady state.