$Al_{2}O_{3}$ thin films were deposited on GaN(0001) by using a Remote Plasma Atomic Layer Deposition(RPALD) technique with a trimethylaluminum(TMA) precursor and oxygen radicals in the temperature range of $25{sim}500^{circ}C$. The growth rate per cycle was varied with the substrate temperature from $1.8{AA}$/cycle at $25^{circ}C$ to $0.8{AA}$/cycle at $500^{circ}C$. The chemical structure of the $Al_{2}O_{3}$ thin films was studied using X-ray photoelectron spectroscopy(XPS). The electrical properties of $Al_{2}O_{3}$/GaN Metal-Insulator-Semiconductor (MIS) capacitor grown at a $300^{circ}C$ process temperature were excellent, a low electrical leakage current density(${sim}10^{-10}A/cm^2$ at 1 MV) at room temperature and a high dielectric constant of about 7.2 with a thinner oxide thickness of 12 nm. The interface trap density($D_{it}$) was estimated using a high-frequency C-V method measured at $300^{circ}C$. These results show that the RPALD technique is an excellent choice for depositing high-quality $Al_{2}O_{3}$ as a Sate dielectric in GaN-based devices.