For the proposes of fragility analysis, a typical configuration of multi-span simply supported concrete box girder bridges are selected as analytical object from the statistics of as-built high-speed railway bridges in China. A set of bridge samples, in which five uncertain parameters are considered, are established using the trial and error method based on the Latin hypercube sampling. A portfolio of recorded ground motions divided into bins are assembled, and matched with bridge samples. Then nonlinear time history analyses are performed to capture the responses of structure. Damage states of bridge components are defined, and probabilistic seismic demand models are formulated by quadratic regression analysis for the ratios of the capacity and demand. Fragility curves of bridge components are developed consequently and the fragility of bridge system is evaluated using a single estimate for the second order bounds method. The results show that PSDMs formulated by quadratic regression are better than that by traditional linear regression. The expansion bearing and the column piers of this bridge type are fragile under earthquake excitation. A single estimate for the second order bounds method is preferable to evaluate the fragility of bridge system, and is easier to use than the first order bounds method.