Graphene has been increasingly used as an effective support for Pt-electrocatalyst in the direct methanol fuel cells (DMFCs). Very recently, it has been found that introducing the defects in graphenes can not only stabilize the Pt-particles on graphene, but also greatly increase the tolerance to CO-poisoning. Here we explored for the first time the influence of graphene-defects on the Pt-electrocatalytic behavior. At the B3LYP and M06 (single-point) levels, the adsorption and the first dehydrogenation (C-H/O-H) of methanol on Pt supported by three types of graphenes, i.e., pristine, in Stone-Wales (SW) defect and in single-vacancy (SV) defect. The calculations revealed that the SV-defect has the most stabilization and CO-tolerance for Pt, compared to SW- and pristine graphenes. However, meanwhile, the SV-defect significantly increases the intrinsic C-H/O-H cleavage barrier, which would deteriorate the electro-catalytic activity of Pt. (C) 2016 Elsevier Ltd. All rights reserved.