In this study, first-principles calculations are performed to investigate the sensitivity of intrinsic graphene sheet (GS) and Cu-doped graphene sheet (Cu-GS) gas nanosensors for adsorbing CO, H2, and H2S gas molecules using QUANTUM ESPRESSO package. The density of states (DOS), net charge transfer, adsorption energy, partial density of states (PDOS), and the most stable adsorption configuration of these molecules on GS and Cu-GS are studied. The results show the weak physical adsorption of the three gas molecules on GS. The strength of interaction between the Cu-GS system and adsorbed gas molecules is higher due to the Cu doping. It is expected that the significant increase in charge transfer and adsorption energy leads to fundamental improvement in the electrical conductivity of the Cu-GS system. The results indicate that the introduction of Cu impurity can improve the gas sensing properties of graphene-based gas nanosensors. Therefore, Cu-GS is more appropriate for detecting gas molecules compared to pure GS. The results in this study are useful for developing the design of gas nanosensors.