By solving the density matrix equation of three-level molecular system, the pulsed laser pumped D2O gas terahertz laser was theoretically studied, the expression of terahertz signal gain coefficient(Gs)and the pumping signal absorption coefficient (Gp) were obtained, the output power density of terahertz laser was calculated numerically by iteration method. The calculation shows that the spectral characteristics of terahertz laser was in full accordance with the stimulated Raman emission. The signal frequency detuning obviously affects the amplification process, and there exists splitting in the curve because of the dipole of D2O gas molecule being disturbed by the field of pumping pulse. The theoretical spectrum is in good agreement with reported experimental results.