Copper-containing mesoporous carbon (Cu-MC) was prepared by a single-step surfactant-templating method. For comparison, copper-impregnated mesoporous carbon (Cu/MC) was also prepared by a surfactant-templating method and a subsequent impregnation method. Rhenium catalysts supported on copper-containing mesoporous carbon and copper-impregnated mesoporous carbon (Re/Cu-MC and Re/Cu/MC, respectively) were then prepared by an incipient wetness method, and they were applied to the liquid-phase hydrogenation of succinic acid to 1,4-butanediol (BDO). It was observed that copper in the Re/Cu-MC catalyst was well incorporated into carbon framework, resulting in higher surface area and larger pore volume than those of Re/Cu/MC catalyst. Therefore, Re/Cu-MC catalyst showed higher copper dispersion than Re/Cu/MC catalyst, although both catalysts retained the same amounts of copper and rhenium. In the liquid-phase hydrogenation of succinic acid to BDO, Re/Cu-MC catalyst showed a better catalytic activity than Re/Cu/MC catalyst. Fine dispersion of copper in the Re/Cu-MC catalyst was responsible for its enhanced catalytic activity.