Magnesium alloys are potentially useful as structural materials due to higher strength/weight ratio, heat conductivity and recyclability compared to other alloys. These alloys have attracted the interest of modern manufacturing such as the automobile, computer, communication and consumer electronic appliances industries. Hence welding techniques are required to be developed for these applications. Laser are known to be an excellent tool for them. This paper presents the laser weldability of AZ31 magnesium alloy with CW Nd:YAG laser. The low viscosity and surface tension of the melt pool make magnesium more difficult to weld than steel. As a result of this study, optimal process parameters could be obtained without weld defects. Also it was certain that cutting methods had influence on butt weldability.