In order to study the effect of road roughness on the off-road average speed of tracked vehicles, a multi-body dynamic model is established. The vibration response index is proposed and the credibility of the model is verified by the test. Based on the experimental design, a simulation model is made to establish the approximate model between vibration response and vehicle speed, road roughness. Taking the threshold value of the vibration response index as the constraint condition, the mathematical relationship between the roughness of the pavement and the speed of vehicle is fitted by the method of target optimization, and the prediction method of the off-road speed under the condition of random and uneven pavement is put forward. The method is used to calculate the test ground, and the results show that the model can reflect the impact of road roughness on the vehicle speed, and provide an effective quantitative means for vehicle mobility prediction.