The energy distribution of electrons transported through an intrinsic AlN film was directly measured as a function of the applied electric field. Following the transport, electrons were extracted into vacuum through a semitransparent Au electrode and their energy distribution was measured using an electron spectrometer. The electron energy distribution featured kinetic energies higher than that of completely thermalized electrons. Transport through 80 nm thick layers indicated the onset of quasi-ballistic transport. This was evidenced by symmetric energy distributions centered at energies above the conduction band minimum for fields greater than 530 kV/cm. Drifted Fermi-Dirac energy distributions were fitted to the measured energy distributions, with the energy scale referenced to the bottom of the AlN conduction band. The drift energy and the carrier temperature were obtained as fitting parameters. Overshoots as high as five times the saturation velocity were observed and a transient length of less than 80 nm was deduced. In addition, the velocity-field characteristic was derived from these observations. This is the first experimental demonstration of this kind of transport in AlN.