The proton exchange membrane is one of the critical parts of a direct methanol fuel cell. High proton conductivity and low methanol permeability are required. To enhance the performance of a direct methanol fuel cell, graphene oxide was incorporated to Nafionmordenite composite membranes to enhance the compatibility and to decrease methanol permeability. It was found that the membrane with silane grafted on graphene oxide treated mordenite with a graphene oxide content of 0.05% presented the highest proton conductivity (0.0560 S.cm(-1), 0.0738 S.cm(-1) and 0.08645 S.cm(-1) at 30, 50, and 70 degrees C, respectively). This was about 1.6-fold of the recast Nafion and commercial Nafion 117 and was about 1.5-fold of that without graphene oxide incorporation. Finally, the operating condition was optimized using response surface methodology and the maximum power density was investigated. Power density of about 4-fold higher than that of Nafion 117 was obtained in this work at 1.84 M and 72 degrees C with a %Error between the model prediction and the fuel cell experiment of 0.082%. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.