Using density functional theory computations, the structures and electronic properties of hydrogenated and fluorinated aluminium nitride (AlN) were systematically investigated. We found that fully hydrogenated AlN (H-AlN-H) is an indirect-bandgap semiconductor which is similar to an AlN monolayer. Interestingly, Janus functionalized AlN (F-AlN-H) is a direct-bandgap semiconductor with a bandgap of 3.076 eV. F-AlN-H bilayer is also a direct-bandgap semiconductor, but its bandgap (only 0.187 eV) is much smaller than that of F-AlN-H monolayer. In addition, the gap values of both the F-AlN-H monolayer and the F-AlN-H bilayer can be continuously modulated by a perpendicular electric field; semiconductor-metal transition can even be obtained by applying a small electric field in the F-AlN-H bilayer. Our results are expected to shed light on the fabrication of electronic and optoelectronic devices based on AlN monolayer.