The photoluminescence (pL) characteristics of hydride vapor phase epiyaxy (HVPE) grown GaN films on $MgAl_{2}O_{4}$ substrate were investigated with several growth conditions. The GaN films on $MgAl_{2}O_{4}$ substrate is autodoped with Mg atoms which thermally out-diffused from substrate lead to a PL characteristics of impurity doped ones. The Mg-related emission band intensity decreased with growth temperature may due to the evaporation of Mg atoms at the GaN film surfaces. and it also decreased with GaN film thicknesses. We can estimate the diffusion coefficient of Mg atoms in GaN under the consideration of diffusion phenomena between two infinite solids lead to a value of D= 2$ imes$$lO^{-10} extrm{cm}^2/sec.