The geometries, stabilities, electronic properties and catalytic capability of the platinum catalyst supported on oxidized graphene (Pt/OG) are investigated using the first-principles density-functional theory. Compared with the oxygen adatom, the hydroxyl molecule adsorbs weakly and aggregates easily on graphene, while the single oxygen adatom will form the epoxy group (EG) on pristine graphene or the oxygen dopant (OD) in defective graphene. The formation of EG and OD are used to model oxidized graphene (OG). The OD at the vacancy site forms the most stable configuration with a small formation energy and large diffusion barrier, indicating that an OD is easier to incorporate into the graphene sheet. The OD sheet as a substrate can effectively enhance the stability of the Pt catalyst as compared with pristine graphene or the graphene sheet with EG. Moreover, the complete CO oxidation reactions on the Pt/OD system include a two-step process with the Langmuir-Hinshelwood (LH) reaction as a starting step followed by the Eley-Rideal (ER) reaction. The results suggest that the OD sheet can be used as the reactive support to control the stability and reactivity of catalysts, which opens up a new avenue for fabrication of low cost and highly efficient graphene-based catalysts.