Terahertz spectra of terbutaline sulfate in the range of 0.2 to 2.2 THz was obtained by THz time-domain spectroscopy. The discrete wavelet transform was applied to de-noising terahertz waveforms. The signal was decomposed into five layers by wavelet decomposition, and then the high-frequency noise signal was eliminated by wavelet reconstruction. Another try was through calculating the standard deviation of the noise signal by the 1-th level signals which got from wavelet decomposition, and then the soft threshold and hard threshold de-noising method was employed respectively. The robustness of these wavelet de-noising methods was testified in this paper, and the absorption and refraction spectra of terbutaline sulfate were got at last. The result of experiment indicts that wavelet can enhance the signal to noise ratio of system and this paper provides a new way for the detection of terbutaline sulfate.