We have obtained green-beam quality of M2 = 6.2 at an average output power of 120 W by intracavity frequency doubling of a diode-side-pumped, Q-switched Nd:YAG rod laser with a repetition rate of 10 kHz and an optical-to-optical conversion efficiency of 15.2%. To achieve high-beam quality at high average power, the laser employs a thermally near-unstable resonator design with two-rod birefringence compensation in an L-shaped flat-flat cavity. The output power fluctuation of the green laser remains less than 0.9% in 4 h.