Bridges are one of the most important infrastructure systems that provide public and economic bases for humankind. It is also widely known that bridges are exposed to a variety of flood-related risk factors such as bridge scour, structural deterioration, and debris accumulation, which can cause structural damage and even failure of bridges through a variety of failure modes. However, flood fragility has not received as much attention as seismic fragility despite the significant amount of damage and costs resulting from flood hazards. There have been few research efforts to estimate the flood fragility of bridges considering various flood-related factors and the corresponding failure modes. Therefore, this study proposes a new approach for bridge flood fragility analysis. To obtain accurate flood fragility estimates, reliability analysis is performed in conjunction with finite element analysis, which can sophisticatedly simulate the structural response of a bridge under a flood by accounting for flood-related risk factors. The proposed approach is applied to a numerical example of an actual bridge in Korea. Flood fragility curves accounting for multiple failure modes, including lack of pier ductility or pile ductility, pier rebar rupture, pile rupture, and deck loss, are derived and presented in this study.