Gamma-phase lithium aluminate (LiAlO2) single crystal is grown by Czochralski pulling method and a-plane LiAlO2(LAO) is chosen as the substrate for subsequent gallium nitride (GaN) epitaxial growth by plasma-assisted molecular beam epitaxy (PAMBE). The lattice mismatch between the nitride and the substrate is greatly reduced due to small lattice mismatch of~0.3% between [0001]GaN and [010]LAO and of~1.7% between [11-20]GaN and [001]LAO in the plane of the substrate LAO(100). Pure hexagonal [10-10]GaN is successfully grown directly on the LAO substrate without buffer layer. Crystal quality and properties are analyzed through a series of measurements, including reflection high-energy electron diffraction (RHEED), field-emission electron microscopy (FESEM), electron backscatter diffraction (EBSD), x-ray diffraction and cathodo luminescence (CL).