Terahertz parametric oscillator (TPO) using KTiOPO4 (KTP) crystal with a noncollinear phase-matching scheme is investigated. Frequency tuning characteristics of terahertz wave (THz-wave) by varying the phase-matching angle and pump wavelength are analyzed. The expression of the effective parametric gain length under the noncollinear phase matching condition is deduced. Parametric gain and absorption characteristics of THz-wave in KTP are theoretically simulated for the first time. The characteristics of KTP for TPO are compared with MgO:LiNbO3. The analyses indicate that KTP is more suitable than MgO:LiNbO3 for TPO.