The strain-induced modulation of the band dispersion and dielectric response of monolayer and bilayer AlN was studied using density functional theory. The results showed that, by applying strain on monolayer and bilayer AlN, the bandgap of these nanostructures can be controlled. Calculations of the dielectric response show that application of in-plane tensile (compressive) strain causes a red (blue) shift in the ε2(ω) spectrum of both monolayer and bilayer AlN. Applying perpendicular strain on bilayer AlN leads to a shift of the valence-band maximum to the Γ -point in the band structure and shift of the peak positions and variation of the peak intensities in the ε2(ω) spectrum. The predicted tunability of the bandgap and dielectric response by strain application may lead to a wide range of applications for monolayer and bilayer AlN nanosheets in electronic and optoelectronic devices.