Frequency tuning characteristics of a THz-wave by varying phase-matching angle and pump wavelength in a noncollinear phase-matching THz-wave parametric oscillator (TPO) are analyzed. A novel scheme to realize the tuning of a THz-wave by moving the cavity mirror forwards and backwards is proposed in a noncollinear phase-matching TPO. The parametric gain coefficients of the THz-wave in a $LiNbO_3$ crystal are explored under different working temperatures. The relationship between the poling period of periodically poled $LiNbO_3$ (PPLN) and the THz-wave frequency under the condition of a quasi-phase-matching configuration is deduced. Such analyses have an impact on the experiments of the TPO.