The stable geometrics and adsorption behaviors of hydroxyl (OH) groups on graphene sheets are investigated using the first-principles calculations. The single hydroxyl adatom has small adsorption energy and diffusion barrier on pristine graphene. The binding strength of the hydroxyl group increases with the coverage, and the aggregations of the hydroxyl groups reduce the structural bucking of graphene sheet. On the graphene with single vacancy (SV-graphene), the large trapping zones mean the adsorbed OH would be easily trapped at the vacancy site. The hydroxyl groups prefer to aggregate on graphene surfaces and form the water molecule, leaving the epoxy group on pristine graphene or oxygen dopant in SV-graphene, which is used to constitute the structural model of oxidized graphene. These results would provide us a useful reference to understand the atomic structure and adsorption property of functional groups on graphene sheets.