Graphene nanoribbons (GNRs) as a quasi-one dimensional (1D) narrow strip of graphene hold great potential for applications in variety of sensors because of π-bonds that can react with chemical elements. Despite outstanding properties, graphene nanoribbons have not fully exploited for variety of application in nanoelectronic and nanosensors due to poor understanding of their physical, electrical properties and basic limitations on the synthesis. Therefore, in order to achieve analytical understanding on the interaction of the gas molecules with GNR surface and gas sensing mechanism, a theoretical method using tight binding model based on nearest neighbour approximation is developed in this study. Additionally, the adsorption effects of NO2 and CO2 gas molecules on the band structure and electrical properties of the GNRFET based gas sensor are investigated. Based on the proposed model numerical simulation is carried out which emphasizes the significant effect of the gas adsorption on the band structure and electrical properties of GNRs. On the other hand, quantum capacitance created between metal gate and channel as a sensing parameter is considered and its variations when GNR exposed to the NO2 and CO2 molecules are analytically modelled. Moreover, the adsorption energy and charge transfer occurred during gas molecules interaction with GNR surface are calculated. Also band structure and I–V characteristics are analysed using first principle calculation based on density functional theory. The current–voltage analysis clearly indicates the changes of the quantum capacitance when exposed to the gas molecules. The results of the proposed model are compared with the available experimental data or data obtained by density functional theory (DFT) calculations and good agreements are observed.