The present invention relates to a process of preparing of a phosphorus-containing phosphorus-alumina support by a sol-gel method and a cobalt/phosphorus-alumina catalyst where cobalt is supported onto the phosphorus-alumina support as an active ingredient. The phosphorus-alumina support is prepared by a sol-gel method and has wide specific surface area with bimodal pore size distribution and high cobalt dispersion, thereby enabling to increase heat and mass transfer, stabilize the structure by modifying the surface property of alumina and decrease the deactivation rate due to the reduced oxidation of cobalt component during the F-T reaction. When Fischer-Tropsch reaction (F-T) is conducted on the catalyst, the catalyst maintains a superior thermal stability, inhibits the deactivation due to water generation during the F-T reaction and also causes relatively high conversion of carbon monoxide and stable selectivity of liquid hydrocarbons.