This paper presents a copula technique for developing seismic fragility curves for an RC (reinforced concrete) isolated continuous girder bridge, by considering earthquake damage indicators such as bridge piers, isolated bearing components, and the main girder of collision damage. The results of this method are compared with those of the limit method of the first-order reliability theory. Meanwhile, the incremental dynamic analysis of the bridge structure under different failure conditions is carried out, and the randomness of the near-fault ground motion and the structural parameters are accounted. Based on the damage index of the isolated bridge under different damage conditions, the seismic fragility curves of each component and the whole isolated bridge are obtained. The research shows that the safety control of the isolated continuous girder bridge structure is mainly affected by the seismic fragility of the isolated bearing, the influence of bridge pier seismic fragility is relatively small, and the probability of beam collision in an isolated bridge is lower than that of a general bridge without isolation bearing. By applying the isolation scheme, the probability of different damage state of the bridge structure is greatly reduced, thus the seismic performance is improved. It also verifies the efficiency and superiority of copula technology. The results will provide a reference for future seismic damage prediction.