The paper delves into the fragility analysis of a long-span continuous rigid frame bridge with high piers under multiple hazards. Taking a bridge of this kind prevalent in a mountainous region as a case study, we in this paper built a finite element model with the Open System for Earthquake Engineering Simulation (OpenSees) software and conducted nonlinear time-history analysis under wind and seismic loads. This was followed by assessing the bridge fragility in the conventional method of single-factor control variable (SFCV) fitting. Meanwhile, we, based on seismic fragility analysis, proposed an approach to fragility assessment under multiple hazards before drawing a comparison between the two. The results showed that in analyzing the demand-capacity ratio (DCR) and disaster intensity regression, we found log-linear regression to be more reasonable. The DCR-based log-linear regression analysis can reliably predict the probability of structural damage under wind and seismic loads, thus reducing calculations and avoiding inaccurate predictions arising from a traditionally inadequate wind speed classification. The proposed analysis can predict and assess the risks of bridges of this type in regions prone to multi-hazard events.