The terahertz absorption spectra of the insensitive explosives RDX and HMX in the spectral range from 0 to 2.5 THz are detected with terahertz time-domain spectroscopy. The terahertz absorption spectra and the characteristic absorption peak of test samples are obtained, and comparing with the absorption spectra measured by other research institutions. The results show that the absorption spectra measured in air environment have strong oscillation due to the absorption of water vapor. So the data measured in the air environment are processed with the wavelet transform to eliminate the influence of water vapor, and this method is feasible.