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The quasi-three-level laser operation of Nd:Gd:LuAG crystal is reported for the first time. The maximum continuous-wave (CW) output power of over more than 3 W was obtained with an optical conversion efficiency of 40.0% and a slope efficiency of 55.5%. With Cr:YAG as the saturable absorber, the passively Q-switched laser was achieved with the maximum average output power, shortest pulse width and pulse energy of 820 mW, 21.3 ns, and 124 μJ, respectively. By using a type-II cut LBO crystal as the intracavity frequency doubler, the maximum output power of 802 mW for CW operation and 331 mW for passively Q-switched operation were achieved at the wavelength of 474 nm.