An approach to structural damage identification based on the change of wavelet sub-band signal energy curvature is proposed. To analyze the vibration responses of the intact and damaged structures, the dyadic discrete wavelet transform is adopted. The signal is then decomposed into different sub-bands at the same time the different modal responses are separated. The damage index of the relative energy curvature difference is defined and used to identify the damage location. The numerical simulation study of a simply supported beam bridge shows that the dyadic discrete wavelet transform can successfully separate the different modal responses into different bands, and the damage index can be used to effectively determine the location of the damage, which cannot be affected by the vibration position and the load size. Finally, the method is verified with the experiment of a simply supported beam bridge model.