This paper presents using density functional method to study nitrogen monoxide (NO) molecule physisorption with various concentrations on armchair graphene nanoribbon (GNR). We calculate the physical and electronic parameters of the GNR after nitrogen monoxide molecules adsorption. The Green’s function method is used to obtain the electronic properties and electrical current through the ribbon. The GNR is considered as a channel of a back-gated field effect transistor (FET) to study the sensing properties of a graphene nanoribbon field effect (GNR-FET) sensor. Results show that the GNR is a suitable sensing layer for NO detection with different concentrations. Also, the current in the channel increases when NO molecules density is increased. To improve the sensitivity of the sensor, we apply a gate voltage to change the Fermi level of the channel. Obtained results prove that by applying back gate voltage to the channel of the sensor, the current and sensitivity of the sensor are improved simultaneously.