In this paper, the transmission spectrum, optical homogeneity, resistance of photore-fraction, frequency-doubling and self-frequency-doubling properties of Nd:Mg: LiNbO3 single crystal grown by us have been studied. A Nd:Mg:LiNbO3 self-frequency-doubled laser pumped by dye laser bas been reported. The self-frequoncy-doubling generation tinder noncritical phase matching has been realized and the second-harmonic generation with 542.2 nm wavelength has been obtained.