AlGaN/AlN/GaN high electron mobility transistor (HEMT) structures with a high-mobility GaN thin layer as a channel are grown on high resistive 6H-SiC substrates by metalorganic chemical vapor deposition. The HEMT structure exhibits a typical two-dimensional electron gas (2DEG) mobility of 1944cm^2/(V·s) at room temperature and 11588cm^2/(V ·s) at 80K with almost equal 2DEG concentrations of about 1.03 × 10^13 cm^-2. High crystal quality of the HEMT structures is confirmed by triple-crystal X-ray diffraction analysis. Atomic force microscopy measurements reveal a smooth AlGaN surface with a root-mean-square roughness of 0.27nm for a scan area of 10μm × 10μm. HEMT devices with 0.8μm gate length and 1.2mm gate width are fabricated using the structures. A maximum drain current density of 957mA/mm and an extrinsic transconductance of 267mS/mm are obtained.