Abstract Graphene biosensors have the potential to be excellent applications of two-dimensional materials, because graphene has high mobility and specific surface area. However, it is difficult to stably obtain consistent responses from graphene biosensors owing to external disturbances and the lack of understanding their sensing mechanism. We propose a graphene biosensor coated with a gas-permeable silicone elastomer, poly(dimethylsiloxane). The elastomer coating allows only the gas molecules to reach the graphene surface, suppressing the disturbances from other factors, and thereby eliciting stable responses to target ammonia molecules in solution. It allowed us to clarify the relationship between ammonia production via urease reactions and conductivity changes of the graphene biosensor. The biosensor responses were modeled using the combination of the dissociation equilibrium of ammonia, Langmuir’s adsorption isotherm, and Michaelis–Menten equation. Findings of this study lay the foundation for practical applications of stable graphene biosensors based on our reasonable response model.