Time‐resolved photoluminescence spectroscopy was performed at 77 K in a GaN (1‐101) grown on a 7 degree off‐axis (001) Si substrate. The sample was grown by metal‐organic‐vapour‐phase‐epitaxy (MOVPE) and was un‐intentionally doped with O, C and Si. By using photoluminescence intensity correlation method, the energy relaxation process of the photogenerated carriers near the band edge was investigated in pico‐second regime. The correlation signal was represented by a single exponential decay curve and the energy relaxation time was determined, which depended strongly on the kinetic energy of the excess carriers. At low energies, the relaxation time was around 700 ps, while it was as short as a few ps at the highest energy under study. The correlation signals obtained for carriers of which kinetic energy was less than 80 meV showed an anti‐correlation behaviour suggesting the occurrence of carrier accumulation. The time constants for the accumulation were of several picoseconds depending on the kinetic energy, which was nearly equal to the decay time constants determined at high energies. This fact shows that the energy relaxation at high energies is controlled by the emission of an LO phonon. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)