In this paper, the terahertz (THz) absorption spectra of a nematic liquid crystal (NLC) cell are estimated via THz time-domain spectroscopy (TDS) using a mode-locked Yb-doped fiber laser as the pump source. The THz-TDS system is implemented by using a dipole antenna as an emitter and a bow tie antenna as a receiver. A THz emission bandwidth exceeding 2.2 THz is achieved corresponding to a free spacing of 220 mm and a signal-to-noise ratio exceeding 30 dB. Subsequently, this system was utilized to measure and analyze the THz absorption spectrum of an E7 NLC cell by applying an electric field. The conclusions experimentally confirmed that the absorption of the specific THz frequency of the cell is inversely proportional to the intensity of the electric field applied to the NLC cell.