In civil engineering, the computer has been widely applied and developed as the advantages of speed and high accuracy, in the last 20 years. This paper describes nonlinear time-history response analysis of bridge structure under strength ground motion. Special seismic analysis program-TDAPIII (Time domain 3-dimensional dynamic Analysis Program) is used in this analysis. Firstly, the direct integration method for solving dynamic problems and the calculation method of fiber element are introduced in this program. Secondly, a five-span continuous viaduct bridge including the foundation, rubber bearing, and superstructure and RC piers is modeled and the dynamic response analysis of model is examined. Lastly, response results of RC bridge piers are evaluated by dynamic/static verification method. It indicates that dynamic analysis of Viaduct Bridge is valid. And these RC piers should be safety under strength ground motion by verification of seismic performance.