Recently reported asynchronous-optical-sampling terahertz (THz) time-domain spectroscopy enables high-resolution spectroscopy due to a long time-delay window. However, a long-lasting tail signal following the main pulse is often measured in a time-domain waveform, resulting in spectral fluctuation above a background noise level on a high-resolution THz amplitude spectrum. Here, we adopt the wavelet power spectrum estimation technique (WPSET) to effectively remove the spectral fluctuation without sacrificing spectral features. Effectiveness of the WPSET is verified by investigating a transmission spectrum of water vapor.