KTiOPO₄ (KTP) crystal is used as the nonlinear medium in a surface-emitted terahertz-wave parametric oscillator for the first time. The oscillating Stokes beam propagates along the x axis of the KTP crystal, the pumping beam propagates with a small incident angle θ(ext) to the x axis, and the polarizations of the pumping beam, the Stokes beam, and the THz wave are along the z axis. When θ(ext) is changed from 1.250° to 6.000°, the THz wave is intermittently tuned from 3.17 to 3.44 THz, from 4.19 to 5.19 THz, and from 5.55 to 6.13 THz. The maximum output of the THz wave is 336 nJ, obtained at 5.72 THz with a pumping energy of 80 mJ. The two frequency gaps, from 3.44 to 4.19 THz and from 5.19 to 5.55 THz, are located in the vicinities of the A₁ modes of 134 and 178.7 cm⁻¹, which are strongly infrared absorbing.