In this article, a high-composition (>35%) thick-barrier (>30 nm) AlGaN/AlN/GaN high-electron-mobility transistor (HEMT) structure grown on a sapphire substrate with ultra-low sheet resistivity (<250 Ω/□) is reported. The optimization of growth conditions, such as reduced deposition rate, and the thickness optimization of different epitaxial layers allowed us to deposit a crack-free high-composition and thick AlGaN barrier layer HEMT structure. A significantly high two-dimensional electron gas (2DEG) density of 1.46 × 1013 cm−2 with a room-temperature mobility of 1710 cm2/V·s was obtained via Hall measurement using the Van der Pauw method. These state-of-the-art results show great potential for high-power Ga-polar HEMT design on sapphire substrates.