Conventional analytical methods in the wavelet domain are used to present an analysis of terahertz (THz) waveguide modes. To obtain THz radiation pulses passing through a waveguide, we build a simple experimental system with a 5-mm-long, 230-\mum-inner-diameter stainless steel waveguide. The single-mode guided signal from the experiments and the multi-mode signal of a similar THz waveguide reported in the literature are analyzed using the continuous wavelet transform (CWT). The results demonstrate that analyzing THz waveguide modes in the wavelet domain not only possesses all the functionality of the traditional THz time-domain spectroscopy (TDS) data processing but also has the ability to unscramble quantitatively and intuitively detailed information about the target samples, such as mode type, cut-off frequency, amplitude distinction, and group velocity.