System interferences such as noise and background information in terahertz time-domain spectroscopy (THz-TDS) add difficulty to spectral signal analysis and affect the accuracy of component identification. In this paper, we proposed an adaptive filter based on a recurrent quantum neural network (RQNN) to process the THz-TDS signal. RQNN is a network architecture guided by quantum mechanics, for adaptive filtering of THz-TDS signal. Six pure substances, ferric sulfate, ferrous sulfate, Prussian blue, agarose, polylysine and sodium of polyaspartic acid were used as test samples. The TDS signals of the six samples were filtered with RQNN and five competing filters. Optical constants including refractive index and absorption coefficient were calculated from raw THz signal and filtered THz signal. Peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were calculated between the optical constants calculated before and after filtering as evaluation indicators. Results revealed that RQNN could better eliminate the noise in THz-TDS signals, and retain the characteristic peaks in the calculated optical constants simultaneously. In terms of PSNR and SSIM, RQNN-filtered THz-TDS signals demonstrated higher values than those of the competing filters. The RQNN proposed in this paper can be used as an adaptive filter for noise filtering and signal extraction of THz-TDS signal, with advantages above traditional filtering algorithms.