We report a tunable quasi-phase-matched optical parametric generator (OPG) with different wedge angles, pumped by a commercially available Q-switched diode-pumped Nd:YVO4 laser with a repetition of 50 kHz. The nonlinear crystal is a periodically poled MgO-doped LiNbO3 (PPMgOLN) with a period of 30 um. A congruent bulk LiNbO3 (LN) with three different wedge angles of 0, 4, and 9 deg. is placed in front of PPMgOLN. Rapid tuning has been achieved by simply moving the LN crystal along its lateral direction and over 60-mW average signal output power was obtained in the whole wavelength tuning range of 1539-1570 nm.