High-quality AlGaN/GaN/AlN heterostructures with thin GaN channel and thick AlN buffer layer were grown by metal organic chemical vapor deposition (MOCVD) on SiC substrate. By analyzing growth modes of GaN films on AlN buffer layers with different thicknesses, it is revealed that film-forming point of GaN grown on AlN buffer increases with the increase in AlN buffer thickness. Accordingly, new growth model of GaN on AlN buffer was proposed, which shows that there is an optimal matching value between Ga source flow rate and AlN thickness when GaN is grown on AlN buffer of different thicknesses. Under optimal conditions, AlGaN/GaN/AlN heterostructures with 120 nm thin GaN channel layer and thick AlN buffer show excellent carrier-limited domain, high crystalline quality, and good transport properties. Results in this work would be useful for preparing high-quality heterostructures on AlN buffer and high electron mobility transistor (HEMT) devices. Moreover, these findings can also be applied to the growth of other hyperfine structures (quantum wells, superlattices, and digital alloys) in the future.