Methanol crossover due to the low selectivity of proton exchange membranes is a long-standing issue in direct methanol fuel cell technology. Here we attempt to address this issue by designing a composite membrane fabricated by sandwiching a monolayer graphene between two thin Nafion membranes to take advantage of monolayer graphene's selective permeability to only protons. The methanol permeability of the present membrane is demonstrated to have a 68.6% decrease in comparison to that of the pristine Nafion membrane. The test in a passive direct methanol fuel cell (DMFC) shows that the designed membrane retains high proton conductivity while substantially suppressing methanol crossover. As a result, the present membrane enables the passive DMFC to exhibit a decent performance even at a methanol concentration as high as 10.0 M. (C) 2016 Elsevier B.V. All rights reserved.