A control strategy with the strong adaptability is crucial to maintain the stable body attitude, when the vehicle is encountering various complex road inputs. This article is based on the theory that the centroid of the cheetah's body always moves in a straight or curved line when running in the wild, and studies the control strategy of the vehicle’s active suspension. Firstly, the relationship matrix between control forces of actuators and virtual control forces that maintains the stabilization of the body attitude is derived, which is the Moore Penrose inverse matrix. Secondly, due to numerous nonlinearities, uncertain factors in the entire vehicle system and complex road conditions, a variable universe fuzzy controller for the stabilization of the vehicle body attitude is proposed. Finally, experiments are conducted with a three-axle heavy emergency rescue vehicle. Experimental results show that compared with the RMS of the vehicle with the passive suspension, the RMS of the pitch angle and the roll angle of the body with the active suspension are reduced by 27.04% and 25.84%, respectively; the RMS of the pitch angular acceleration, the roll angular acceleration and the vertical displacement acceleration of the body with the active suspension are reduced by 20.05%, 27.12% and 20.03%, respectively. The proposed controller has the high adaptability to the road input excitation, thereby improving the adaptability of vehicles to various road conditions effectively, maintaining the stable body attitude while driving, improving the “comfort” and the “safety” of passengers and on-board rescue equipment, and greatly improving the rescue efficiency of the vehicle.