Diamond/III-V nitride semiconductor heterostructure appears promising not only for high-efficiency deep-UV light emitting diodes (LEDs) but also for high output power field-effect transistors (FETs). However, diamond has a diamond crystal structure, while III-V nitride semiconductors have a wurtzite crystal structure. Due to the deference in the crystal structures, single-crystal III-V nitride growth on diamond substrate was difficult. In this study, we obtained the single-crystal aluminum nitride (AlN) (0001) layers on diamond substrates by using (111) diamond surface orientation and preventing the formation of the interface layer. Then, we revealed the heteroepitaxial growth mechanism and proposed an atomic arrangement model at the diamond/AlN heterointerface. Furthermore, we demonstrated a p-type diamond/n-type AlN heterojunction diode and successfully observed band-edge emission from diamond. In addition, an AlGaN/GaN heterostructure with two-dimensional electron gas (2DEG) was grown on diamond (111) using the single-crystal AlN buffer layer.