A high‐electron‐mobility transistor (HEMT) structure consisting of a strain‐engineered quaternary AlGaInN barrier layer on an unintentionally doped (UID) GaN channel layer is grown on a single‐crystal (SC) AlN substrate by metal–organic chemical vapor deposition and subjected to the device fabrication and characterization. It is showed in DC static measurement results that the fabricated HEMTs exhibit good current–voltage (I–V) characteristics without large negative resistance even at high‐current operations. Pulse I–V measurements results indicate that the fabricated devices show a low‐drain–current collapse as unpassivated GaN HEMTs and that it is further improved by applying an Al2O3 surface passivation. The present results signify promising prospects of AlGaInN/GaN HEMTs on SC‐AlN toward future high‐power radio‐frequency (RF) applications.