Using first-principles calculation, we studied the role of defects in tuning the adsorption of CO molecule over graphene-supported Co-13 cluster, with a focus on the adsorption geometries and stabilities, electronic properties. It is shown that Co-13-graphene interfaces exhibit covalent bonding characters with the most stable on C-vacancies support. The supports stabilize the adsorption of both intact and dissociative CO molecule over Co-13/graphene composites, especially the vacancies and N-doped supports outperform the others. Moreover, intact CO molecule is energetically more favorable than its dissociative adsorbing over all the composites, and notably doping of B or P atom in support gives rise to quite similar effects. Overall, C-vacancies and atomic N-embedded in graphene supports can effectively improve CO adsorption on cobalt cluster, beneficial for CO conversion in Fischer-Tropsch synthesis.