The simulation experiment on the laser cutting of the AZ31B magnesium aluminum alloys is conducted based on the thermodynamic equations and it is found that the cutting quality of samples is better when the laser cutting speed is 8 mm·s-1. The process experiment on the laser cutting of the 1.0-mm-thick AZ31B magnesium aluminum alloys is carried out and the single-factor experimental data related to the effects of laser power, cutting speed and defocusing is obtained. The scheme of three-factor orthognal experiment is also proposed. The optimum process parameters for a laser cutting of the 1.0-mm-thick AZ31B magnesium aluminum alloys are a laser power of 120 W, a cutting speed of 0.5 m·min-1, and a defocusing of 1.2 mm, which are basically consistent with the theoretical calculation values.