A novel damage detection approach is proposed in this study for a continuous girder bridge in which support reaction influence lines (ILs) are adopted. First, the relationship between the local damage of a continuous girder bridge and a damage index, based on support reaction ILs, is established through analytical derivation. Subsequently, the sensitivity of a support reaction IL-based damage index is analyzed using Dempster-Shafer(D-S) evidence theory, and it shows that the support reaction IL-based damage index is more noise-resistant if more support reaction ILs from a variety of locations are used. Three case studies (a simple numerical study of a two-span continuous beam, a laboratory experimental study of a two-span aluminum beam, and a complicated numerical study of a continuous girder bridge in Xiamen) have been conducted to validate the effectiveness of the proposed method in different damage scenarios, including single damage and multiple damages. Satisfactory damage identification results can be obtained even in high-level measurement noise conditions, showing that the proposed approach offers a promising field detection technique for identifying local structural damages in continuous girder bridges.