Since the major advantage of (1 1 (2) over bar 0) sapphire substrate is the ability to easily form cleaved facets, which is important for the fabrication of edge-emitting lasers, it is meaningful to investigate the GaN epilayer grown on (1 1 (2) over bar0) sapphire substrate. X-ray diffraction (XRD) measurement indicates that the GaN growth is still along (0 0 0 1) direction even on (1 1 0) sapphire substrate. However, compared with the GaN grown on (0 0 0 1) sapphire substrate, the GaN layer on (1 1 0) sapphire substrate shows a larger c-axis lattice constant and smaller a-axis lattice constant, which indicates that there exists an enhanced lattice-mismatch compared with the case on (0 0 0 1) sapphire substrate. The detailed XRD measurement indicates that the strain exerted on the GaN on (1 1 0) sapphire substrate is increased by 0.03% compared with that on (0 0 0 1) sapphire substrate. Furthermore, the low-temperature photoluminescence indicates that the GaN on ( 1 1 0) sapphire substrate shows a 4.5 meV blue-shift compared with the GaN on (0 0 0 1) sapphire substrate, which is in a good agreement with our calculation based on the lattice-mismatch induced strain model. A crystallographic depict is proposed for a good explanation of a GaN layer growth on (1 1 (2) over bar 0) sapphire substrate. By selective-area diffraction (SAD) and high-resolution transmission electron microscopy measurement (HREM), the inplane orientation relationship is determined to be (1 1 (2) over bar 0)(GaN) //(1 (1) over bar 0 0)(sapphire) and (1 (1) over bar0 0)(GaN) // (0 0 0 1)(sapphire) which also shows that a larger lattice-mismatch between (0 0 0 1) GaN and (I I 0) sapphire substrate occurs and thus gives rise to an enhanced compressive strain. In turn, it supports our above discussion.