This study is related to the laser weldability of AZ31B magnesium alloy, an all-purpose wrought alloy with good strength and ductility. In general, AZ31B is classified into AZ31B-H24 and AZ31B-O depending on temper designation. Thus, in this study, the laser weldability of AZ31B-H24 and AZ31B-O was investigated and compared. CW Nd:YAG laser was used to produce bead and butt joints. And the effects of welding conditions on the weldability of these joints were examined in detail. As a result of this study, AZ31B-H24 was found to have thinner oxide film and smaller grain size compared with AZ31B-O. Due to such difference, in bead welding, AZ31B-H24 had more wide welding range for full penetration compared with AZ31B-O. Furthermore, it was also confirmed that AZ31B-H24 and AZ31B-O have different welding conditions to obtain stable keyhole in butt welding.