Based on the semi-classical density matrix theory,the gain coefficients of infrared (IR) pumping signal and submillimeter wave (SMMW) laser signal for a three-energy-level system in single-longitudinal-mode (SLM) and in multi-longitudinal-mode (MLM) pulse optically pumped D2O SMMW laser are deduced. The spectral characteristics and output power are calculated by numerical iteration method. The laser processes and the fine structures in spectral characteristics are studied and compared in detail. MLM optically pumped D2O superradiant laser produces a wider SMMW laser line than SLM pumped laser does. In both SLM and MLM optically pumped D2O cavity lasers,SMMW laser lines broaden further and narrow peaks will appear in their spectrum. These narrow peaks correspond to the MLM structure of the SMMW laser line. The wide band spectrum and MLM structure characteristics provide a theoretical basis for frequency tunable SMMW laser.