Abstract: The continuous wavelet transform (CWT) by a Mexican hat wavelet having two vanishing moments is applied to the first mode shape difference of a structure under the health and damage state. A damage index is presented based on the wavelet singularity detection theory and mode curvature conception, and the damage location is detected by the maximum of the index. To test the effectiveness of the proposed method, numerical simulation and experiment analysis are performed on a cantilever beam. Numerical simulation results show that the index can exactly detect the location of the damage. The relation between Lipschitz exponent and damage extent is analyzed based on the index maximum.