Abstract: For typical high order modes of Hermite-Gaussian beam,the effect of frequency doubling on beam quality factor and the space distribution was studied by means of calculation and experiments.The beam quality of the frequency doubled beam was deteriorated seriously with the beam quality of basic frequency reducing.The beam quality of the frequency doubled beam was invariant when the radius of the basic beam with the same beam quality was variant in the crystal surface.Green power of 49.5W was generated with a 15kHz repetition rate by intracavity frequency doubling of a diode-pumped Nd:YAG laser.The beam quality factor of the frequency doubled beam was 10.2 with the basic beam quality factor of M2=4.93.The result of experiment was the same with the theoretical calculation.