The absorption coefficient of magnesium-doped near-stoichiometric lithium niobate crystal is measured by terahertz time-domain spectroscopy in a frequency range of 0.2 THz^0.9 THz at room temperature. The absorption coefficient is modulated by external optical pump fields. Experimental results show that the absorption coefficient of near-SLN:Mg crystal is approximately in a range of 22 cm- 1_35 cm- 1 in a frequency range of 0.2 THz-0.9 THz and tunable up to nearly 15%. Further theoretical analysis reveals that the variation of absorption coefficient is related to the number of light-induced carriers, domain reversal process, and OH- absorption in this crystal.