Signal processing and analysis of structural vibration measurements are key components of structural damage detection (SDD) in structural health monitoring (SHM). The goal of signal processing is to extract subtle changes in the measured signals, which can be used to infer changes in structural parameters and damage. Time-frequency analysis is one of the most popular characterization methods for studying non-stationary vibration signals. In this article, the local time-frequency transform (LTFT) is applied and evaluated to calculate the time-domain signals because of its excellent time-frequency energy distribution properties. The LTFT matches the input data by the Fourier basis in an inverse problem framework and uses the least squares method to solve the time-varying Fourier coefficients. Subsequently, it defines the time-frequency spectrum as the calculated time-varying Fourier coefficients. While the LTFT has been used in the field of geophysics for seismic data processing, its application to structural vibration signals is novel. Both synthetic signals as well as signals collected from a large-scale laboratory test of a reinforced concrete girder were processed with the LTFT and compared with Rényi entropy for quantifying the time-frequency spectrum, the time-frequency resolution abilities of short time Fourier transform (STFT), and S transform (ST). The results show that the LTFT is superior to the traditional time-frequency analysis schemes, in that it is more effective in identifying the energy changes in the time-frequency spectrum before and after structural damage in the form of cracking has occurred. At the same time, it provides high-precision time-frequency resolution and excellent noise suppression abilities. The effectiveness and feasibility of the LTFT applied to the synthetic and experimental signals are verified.