An emission, named (D 2 0 ,X), located at ϳ3.48 eV at low temperature, in the near-band-edge spectrum of GaN, was investigated by photoluminescence ͑PL͒. This (D 2 0 ,X) emission is close in energy to the well-studied neutral-donor-bound-exciton (D 0 ,X) line in GaN. They are distinguished by a variety of PL measurements in this study. Excitation power and temperature-dependent studies indicate that this emission is related to a bound exciton complex. Annealing at a relatively low temperature ϳ440°C results in a dramatic reduction of the PL intensity of this emission. A model is proposed that the exciton-binding center responsible for the (D 2 0 ,X) emission consists of a ͑shallow͒ donor-hydrogen complex that is formed in the GaN epilayer during the growth. The annealing at 440°C results in the dissociation of this complex and thus reduces the PL intensity of the (D 2 0 ,X) emission.