We performed a comprehensive study of catalytic activities of subnanometer Au clusters supported on TiO2(110) surface (Au-n/TiO2, n = 1-4, 7, 16-20) by means of density functional theory (DFT) calculations and microkinetics analysis. The creditability of the chosen DFT/microkienetics methodologies was demonstrated by the very good agreement between predicted catalytic activities with experimental measurement (J. Am. Chem. Soc, 2004, 126, 5682-5483) for the Au1-4/TiO2 and Au7/TiO2 benchmark systems. For the first time, the size- and shape-dependent catalytic activities of the subnanometer Au clusters (Au-16-Au-20) on TiO2 supports were systematically investigated. We found that catalytic activities of the Au-n/TiO2 systems increase with the size n up to Au-18, for which the hollow-cage Au-18 isomer exhibits highest activity for the CO oxidation, with a reaction rate similar to 30 times higher than that of Au-7/TiO2 system. In stark contrast, the pyramidal isomer of Au-18 exhibits much lower activity comparable to the Au3-4/TiO2 systems. Moreover, we found that the hollow-cage Au-18 is robust upon the soft-landing with an impact velocity of 200 m/s to the TiO2 substrate, and also exhibits thermal stability upon CO and O-2 co-adsorption. The larger pyramidal Au-19 and Au-20 clusters (on the TiO2 support) display much lower reaction rates than the pyramidal Au-18. Results of rate of reactions for unsupported (gas-phase) and supported Au clusters can be correlated by a contour plot that illustrates the dependence of the reaction rates on the CO and O-2 adsorption energies. With the TiO2 support, however, the catalytic activities can be greatly enhanced due to the weaker adsorption of CO on the TiO2 support than on the Au clusters, thereby not only the ratio of O-2/CO adsorption energy and the probability for the O-2 to occupy the Ti sites are increased but also the requirement for meeting the critical line becomes weaker. The obtained contour plot not only can provide guidance for the theoretical investigation of catalytic activity on other metal cluster/support systems, but also assist experimental design of optimal metal cluster/support systems to achieve higher catalytic efficiency.