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Glucose oxidase (GOx) is one of the most widely investigated enzymes in the field of bioelectrochemistry. It is mainly used for the detection of glucose in solutions and enzyme-based biofuel cells. On the basis of the combination of GOx with graphene, novel nanodevices exceeding conventional limits can be developed. To develop a hybrid enzyme–graphene nanodevice with a good performance, it is important that GOx is deposited well on the graphene surface while maintaining its structure and not impeding the oxidation activity of the GOx. In this study, we propose a method to improve the stability of GOx and secure its immobility on the graphene sheet and its glucose-binding affinity by single-point mutation of GOx using molecular dynamics simulations. We confirm that the structural stability, immobility, and substrate binding affinity of GOx can be modified by changing the hydrophobicity of a key residue. We demonstrate that biosensors or biofuel cells can be redesigned and their properties can be improved by using molecular dynamics simulation.