To choose a proper functional among the diverse density functional approximations of the electronic exchange-correlation energy for a given system is the basis for obtaining accurate results of theoretical calculations. In this work, we first propose an approach by comparing the calculated ΔE0 with the theoretical reference data based on the corresponding experimental results in a gas phase reaction. With ΔE0 being a criterion, the three most typical and popular exchange-correlation functionals (PW91, PBE and RPBE) were systematically compared in terms of the typical Fischer-Tropsch synthesis reactions in the gas phase. In addition, verifications of the geometrical and electronic properties of modeling catalysts, as well as the adsorption behavior of a typical probe molecule on modeling catalysts are also suggested for further screening of proper functionals. After a systematic comparison of CO adsorption behavior on Co(0001) calculated by PW91, PBE, and RPBE, the RPBE functional was found to be better than the other two in view of FTS reactions in gas phase and CO adsorption behaviors on a cobalt surface. The present work shows the general implications for choosing a reliable exchange-correlation functional in the computational catalysis of a surface.