By performing first-principles calculations, we demonstrate the electronic structure, the transport properties, and the adsorption effect of A-Z-A graphene nanoribons field effect transistor. It is concluded that the pure A-Z-A GNR-FET has typical bipolar characteristics, and energy gaps will become smaller due to the adsorbed molecule. For the adsorption of H, N2, NO2, H2O, SO2, O2 and NO, A-Z-A GNR-FET remains typical bipolar characteristic, but shows a little difference in transport property after it has adsorbed different types of molecles. For the adsorption of OH, transport property changes totally and does not have a bipolar characteristic any more. These results may contribute to the implementation of gas detector based on GNRs and the design of GNR-FET applied in complex environments.