Considerable research has been carried out to study the laser welding of magnesium alloys. However, the studies are mainly devoted to butt welding, and there has been limited information in the published literature concerning the bead-on-plate laser welding of AZ91D, even though bead-on-plate welding is required for the repair of cast AZ91D parts with surface defects. In the present investigation, surface cracking of the weld metal was observed when an AZ91D magnesium alloy was bead-on-plate welded using the laser welding method. This paper presents the experimental results and analyses to show that the cracking is “solidification cracking” initiated from the weld surface under high thermal stresses. This is in contrast to the “liquation cracking” observed in heat affected zones in tungsten inert gas welding of the same magnesium alloy. Laser power was found to be one of the main factors affecting the distance of the crack propagation. The higher laser power resulted in longer crack propagation distance into the weld metal. It is demonstrated that hot cracking could be avoided by lowering the laser power and welding speed.