To analyze the dynamic response of the deck pavement of continuous box girder bridge with variable section corrugated steel webs (CBB) under moving loads, a three-dimensional (3D) finite element model of three-span CBB superstructure was established using the finite element software ABAQUS. The validity of the 3D finite element model was verified by the field static load test data. Five vehicle speeds (40 km/h, 60 km/h, 80 km/h, 100 km/h, and 120 km/h), four types of axle loads (5 kN, 25 kN, 30 kN, and 40 kN), and three kinds of load positions were selected. The dynamic responses of the CBB deck pavement, displacement, stress, acceleration, and impact coefficient were calculated. The results showed that under the action of moving loads, the maximum values of vertical displacement and vertical stress appeared on the top surface of deck pavement. The longitudinal shear stress of deck pavement of CBB increased with the increase of pavement depth, and it reached the maximum value at the top of concrete pavement. With the increase of vehicle speed, the impact coefficient, vertical displacement, and transverse stress of the top surface of deck pavement gradually decreased, which indicated that the stress of deck pavement was significantly impacted by the vehicle speed and axle load, while its vertical displacement was less influenced. Under the eccentric load, the large transverse torsion would be produced in the CBB and the more the load deviates from the centerline of the cross section of the CBB, the greater the vibration amplitude of the vertical acceleration generated by the mid-span node on the surface of the deck pavement. Therefore, the low vehicle speed and eccentric load had a great impact on the structural safety response of deck pavement. In practical engineering, it is necessary to avoid vehicles driving at low speeds on one side of the bridge.