Atomically thin two-dimensional (2D) materials are ideal gas sensing materials for achieving an ultra-low detection limit, due to the high surface-to-volume ratio, low electronic noise and sensitively tunable Fermi level. However, the sensitivity of 2D materials to their surrounding environment may also severely degrade the long-term stability of sensing devices, since most of them use the same 2D material flake as both the sensing and conduction material. In this work, we report a gas sensor based on a 2D material field effect transistor (FET) which uses few-layer black phosphorus (BP), boron nitride (BN) and molybdenum disulfide (MoS2) as the top-gate, dielectric layer and conduction channel, respectively. In this device configuration, the top-gate of BP with a superior gas adsorption capability serves as the sensing material, while the conduction channel of MoS2 is isolated from ambient environment by the coverage of the BN dielectric layer. The separation of the sensing and conduction materials not only improves the long-term stability of the device, but also enables us to use different materials for gas adsorption and conduction purposes to achieve optimum sensing performances. In addition, the adsorption kinetics of the gas molecules on the sensing channel can be sensitively detected by the current/resistance variation of the conduction channel, since the adsorbed gas molecules can effectively tune the Fermi level of sensing and conduction materials (BP and MoS2, respectively) through band alignment. We experimentally demonstrated that the proposed 2D material FET not only achieved a detection limit of 3.3 ppb to NO2, but was also capable to differentiate oxidizing and reducing gases.