Based on the technology of the non-collinear phase-matching about three-wave interaction in uniaxial crystal, the performance of nonlinear crystal MgO:LiNbO 3 (MgO:LN) including the phase-matching angles, effective nonlinear coefficient and THz-wave gain as well as its absorption coefficients are theoretically discussed under e-ee type phase-matching condition. And an external cavity is developed for terahertz-wave parametric oscillators pumped by picosecond laser (ps-TPOs). For optimizing the ps-TPOs performance, the focusing spot size in MgO:LN crystal, the geometric size of the MgO:LN crystal, the conversion efficiencies, and the stability of the THz-wave generation are designed and calculated. The calculated results provide a comprehensive theoretical basis for the ps-TPOs using difference-frequency generation (DFG) method and optimal performance to generate widely tunable terahertz waves in MgO:LN crystal.