The current collapse transient behavior of a practical submicron AlGaN/GaN heterostructure field effect transistor (HFET) is investigated, and its mechanism is proposed. First, the steady-state and transient characteristics of the Schottky diode obtained by connecting the source and drain electrodes of the transistor have been investigated. The steady-state characteristics can be explained by the thin surface barrier model, indicating the presence of tunneling injection of electrons. Turn-on and turn-off transient characteristics of the reverse current of Schottky diode showed very slow nonexponential transients covering six orders of magnitude of time scale from milliseconds to thousands of seconds. They are very similar to those of a large planar Schottky diode studied recently by the authors. The HFET device showed a clear current collapse behavior after a gate stress beyond pinch off. Pulsed gate stress visualized drain current transients which again included very slow nonexponential transients covering six orders of magnitude of time scale. The whole experimental results are explained consistently by a model in which the current collapse is due to surface state charging near the source side and drain side of the gate edge where its rate limiting process is not the usual Shockley-Read-Hall capture-emission process but the dispersive electron transport through the surface states by time-continual hopping, which is triggered by the tunneling injection process at the gate edge.