Dissimilar joining of molybdenum (Mo) to titanium (Ti) is of great significance to the design and fabrication of high-temperature facilities. However, few reports were found about fusion joining of these two metals. The objective of this paper is to assess the feasibility of laser beam welding (LBW) of 2 mm-thick molybdenum and titanium. The effects of laser beam offset on the laser dissimilar joint of pure molybdenum to pure titanium were analyzed in terms of microstructure, chemical composition, microhardness, and tensile behavior. The results showed that the weld appearance improved with the increase of the offset. The fusion zone was strengthened because of the solid solution of these two elements. The mechanical properties of samples increased firstly and then decreased with the increasing of offset. When the laser beam irradiated on the titanium plate and the center of the laser spot was 0.5 mm away from the Mo/Ti interface, the joint performed the highest tensile strength, which was about 70% that of titanium base metal. LBW was demonstrated to be a promising method to join dissimilar Mo/Ti joint.