To explore the effects of typical uncertainty factors on the seismic performance of small-and medium-span bridges during design, construction, and service, a four-span continuous small box girder bridge was taken as the engineering background, and a nonlinear dynamic model was built based on OpenSees. The influence mechanisms of seismic uncertainty, modeling parameter uncertainty, and capacity uncertainty on the seismic demand of key components were analyzed. On this basis, combined with the theory of fragility analysis, the linkage effect of the above uncertainty factors in the establishment of component fragility curves was explored, and then the degree of influence of each type of uncertainty factors on the analysis of structural seismic performance was quantified. 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. The 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. The 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.