To explore the influence of various uncertainties on the seismic performance of small and medium span bridges during design, construction and service, a four-span continuous small box girder bridge is taken as the engineering background, and a nonlinear dynamic model is built based on OpenSees, the effects of seismic wave uncertainty, modeling parameter uncertainty and component seismic capacity uncertainty on structural seismic response, establishment of component vulnerability curves, component seismic performance and system seismic capacity are considered through fragility analysis, and the effects of various uncertainties on structural seismic performance analysis are quantified by considering the linkage effects among uncertainties. The results show that the differences in the seismic hysteresis curves of the components are mainly caused by the uncertainties of the modeling parameters, while the differences in the peak seismic response are mainly caused by the combined uncertainties of ground shaking and modeling parameters; modeling parameter uncertainty and component seismic capacity uncertainty can lead to an increase in the probability of structural damage, which consequently makes some components unable to meet the required damage state; consideration of the uncertainty factor increases the probability of failure of the bridge system susceptibility curve, and the effect of uncertainty increases as the degree of damage deepens, biasing the analysis results by more than 30 percent.