The stresses of the pavement systems of the steel-concrete composite continuous beam deck are very complicated， and the early damage of the deck pavement systems is closely related to the dynamic response under the vehicle load. A rubber tire finite element model and a three-span steel-concrete composite continuous beam model are established in this paper. The rubber tire adopts the Yeoh model， and the bridge deck pavement material （asphalt mixture） adopts the generalized Maxwell model. Moreover， the dynamic force of the rear axle suspension of the vehicle is applied to the rubber tires. The vertical deflection， vertical stress， longitudinal stress， transverse stress， and displacement spectrum of each pavement layer of the bridge deck can be solved comparing with the moving load. The results show that the vertical deflections of each span of the three-span steel-concrete composite beam are 21.3%， 4.7%， and 8.0%， respectively， larger than the moving load under the action of tire rolling； the vertical deflection of the longitudinal beam is 8.9% smaller than that of the deck pavement. The stress change trend of the upper layer is similar to that of the cement concrete layer， and the stress changes of the lower layer are more complicated. The displacement response frequency of the upper layer is concentrated in the range of 0~6 Hz. The above data have great guiding significance for structural optimization of bridge deck pavement.