Disclosed herein is a process of producing high purity and high yield dimethylnaphthalene by dehydrogenating a dimethyltetralin isomer using a metal catalyst for dehydrogenation. The metal catalyst contains a carrier selected from alumina (Al.sub.2O.sub.3), silica (SiO.sub.2), a silica-alumina mixture and zeolite. The metal catalyst also contains 0.05 to 2.5% by weight of platinum (Pt), 0.1 to 3.0% by weight of tin (Sn) or indium (In), 0.5 to 15.0% by weight of at least one selected from the group consisting of potassium (K), magnesium (Mg) and cesium (Cs), 0.3 to 3.0% by weight of chlorine, and 0.01 to 3.0 % by weight of zinc (Zn) or gallium (Ga) as active components based on an element weight of the final catalyst.