Since response signals of time-varying bridges exhibit non-stationary characteristics, new time-varying damage indexes, including the maximum change ratio of auto power spectrum (MCRAPS) of the first order intrinsic mode function and the wavelet energy change rate (WCR) of the first order intrinsic mode function, are proposed to detect damages. First, the wavelet threshold denoising method is introduced to reduce noises from original response signals. Then, the first two order intrinsic mode functions (IMF1 and IMF2) are extracted by the analytic modal decomposition theorem and the index of MCRAPS is proposed to detect damage locations. Based on the effective detection of damage locations, the decomposed IMF1 and IMF2 are linearly mixed and then separated by fast independent component analysis (FastICA) to obtain more independent IMF1. Aiming to detect time-varying damages, the new independent IMF1 is used to present WCR by continuous wavelet transform and time window. A dynamic test of a time-varying simply supported steel bridge with moving loads is designed to verify the two proposed damage indexes. The results demonstrate that they can effectively detect damage locations and structural time-varying damages, respectively.