Usually the geological and the climate environmental conditions are considered in designing bridge, but the requirements according to antiknock design for bridge structures are neglected. In order to investigate the dynamic response and damage process of bridge under blast loading, the dynamic response of continuous rigid frame bridge suffering blast loading was simulated numerically by LS-DYNA software, and the characteristics of shock wave propagating in air were analyzed. Also, the response of displacement and the Von-Mises stress distribution around the middle of bridge were obtained, and then the failure state and collapse process of the bridge were showed. Based on the Tuler-Butcher damage rule, the damage accumulation curves of specified elements were obtained. The calculative method and results are referenced for the engineering practice.