The electronic and optical properties of ZnO/GaN-core/shell heterostructures are studied by using the first-principles method based on density functional theory. The results show that the top of valence bands and the bottom of conduction bands for the ［101－0］ and ［112－0］ crystal plane of heterostructures are mainly contributed by the nitrogen and zinc atoms, respectively. The heterostructures with ［101－0］ lateral facets have the similar imaginary parts of dielectric functions (ε2) curves, which are all electronic transitions between the states from nitrogen at valence bands and the states from zinc at conduction bands. However, the peaks of the ε2 curves shift slightly depending on the thickness of the core and shell. In contrast, the ε2 curve for the heterostructures with ［112－0］ lateral facets is significantly different from the cases with ［101－0］ lateral factets.There is a new peak related to the transition between the states from gallium and the states from nitrogen. Therefore, the optical properties of the ZnO/GaN-core/shell heterostructures can be tuned by controlling the lateral facets of the heterostructures.The current work is available for the applications in light emitting device,photoelectric solar cell,and biological detection.