With the point cloud data of box girder obtained by the theory of structure from motion (SFM) algorithm chosen as the research background, a damage identification method based on characteristic curvature and improved wavelet threshold de-noising algorithm is presented. Firstly, the static load test is carried out for the full-scale box girder model, and after the cracking damage, the discrete point cloud data on the surface of the box girder are obtained through the SFM theory. According to the basic hypothesis, deformation is mainly caused by the bending moment, and micro damage has no effect on stress redistribution. Therefore, a conclusion can be made that the curvature is sensitive to the structural damage. Then, a characteristic curvature damage identification method, which is based on point cloud chord length, is used to solve the characteristic curvature of the specified section of the box girder. It is found that there are a large number of point cloud noise signals in the characteristic curvature, and on this basis, a new wavelet de-noising method established upon the threshold function is proposed. Finally, the damage index revealed from the characteristic curvature after de-noising in the specified section is compared with the actual damage location of the box girder. The results show that by combining the characteristic curvature algorithm based on the chord length of scattered point cloud with the improved wavelet threshold de-noising function, the structural surface crack damage based on spatial point cloud data can be identified. Especially, in consideration of noise interference, the improved wavelet threshold de-noising function proposed in this paper can effectively suppress the high frequency noise signal in the characteristic curvature and preserve 506 the low-frequency signal of damage in the damage area. Thus, the accuracy and sensitivity of the damage identification method based on the characteristic curvature are guaranteed. This method has the potential to be applied to structural health monitoring, since it can provide a new technical method for the early warning of the beam structure bridge.