We developed a simple method to improve the stability of organic field-effect transistors (OFETs) with bilayer gate dielectrics. The bilayer gate dielectric comprises an amorphous fluoropolymer (CYTOP) layer and an Al2O3-HfO2 nanolaminate (NL) grown by the atomic layer deposition (ALD) technique. In the OFETs with bilayer gate dielectrics, two aging mechanisms exist, and they cause the shifts of threshold voltage in opposite directions during long-term operation. By engineering the bilayer gate dielectric, the effects of these two mechanisms can compensate, leading to devices with remarkable operational stability that is comparable or superior to that of commercial inorganic counterparts. The NL grown by ALD shows excellent encapsulation property and improves the environmental stability of the OFETs. The devices are tested by exposing the devices to high temperature and high moisture conditions (i.e., the standard 85/85 condition, meaning 85°C and 85% relative humidity). The results of OFETs with CYTOP/NL bilayer gate dielectrics are presented and compared to those OFETs with Al2O3 gate dielectrics.