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This paper investigates the performances of terahertz-wave parametric oscillators (TPOs) based on the LiNbO3 crystal at different pump wavelengths. The calculated results show that TPO characteristics, including the frequency tuning range, the THz-wave gain and the stability of THz-wave output direction based on the Si-prism coupler, can be significantly improved by using a short-wavelength pump. It also demonstrates that a long-wavelength-pump allows the employment of a short TPO cavity due to an enlarged phase-matching angle, that is, an increased angular separation between the pump and oscillated Stokes beams under the THz-wave generation at a specific frequency. The study provides an useful guide and a theoretical basis for the further improvement of TPO systems.