To ensure bridge safety, the flood risk analysis is significant important. However, due to the small size and large number of piers in the short-distance multi-bridge system, the extremely long calculation time and low efficiency of the numerical model are induced by the small mesh size and large mesh number. In this paper, a flood risk assessment model of the multi-bridge system with short distance was established to improve the calculation efficiency based on the finite volume method combined with the Delaunay mesh adaptive refinement method. The calculated water level with refined and non-refined mesh was compared with the experimental data of a partial failure dam break test case and Shukry experiment of open channel bend flow. The calculated water level results are in good agreement with the experimental data. In addition, the mesh refinement model improved the calculation efficiency by more than 73% with ensuring the calculation accuracy. Finally, the flood risk of a real multi-bridge system with short distance was evaluated by using the numerical model. The calculated results shown that, different from the general flow law, the water level in the upstream and downstream channel of Bridge 2 rose with a maximum difference value of 0.326 m while the water level in the far downstream channel of Bridge 2 dropped result from the construction of Bridge 2 on the basis of the Bridges 1, 3 and 4. The construction of Bridge 2 also increased the flow velocity around Bridge 3 with maximum 0.013 m/s. This study provides a new tool and technical reference for flood risk analyses of similar multi-bridge system with short distance.