GaN films were grown for various Mg doping concentrations in metal-organic chemical vapor deposition. Below the Mg concentration of 10$^{19}$ ㎤, the thermally annealed sample shows the compensated phase to n-type GaN in Hall measurement. In the MB concentration of 4$ imes$10$^{19}$ ㎤ corresponding to the hole carrier concentration of 2.6$ imes$1$^{19}$ ㎤ there exists a photoluminescence center of the donor and the acceptor pair transition of the 3.28-eV band. This center is correlated with the defects for a shallow donor of the $V_{Ga}$ and for an acceptor of $Mg_{Ga}$ . The acceptor level shows the binding energy of 0.2-0.25 eV, which was observed by the photon energy of the photocurrent signal of 3.02-3.31 eV. Above the Mg concentration of 4$ imes$10$^{19}$ ㎤, both the Mg doping level and Mg concentration were saturated and there Is a photoluminescence center of a deep donor and an acceptor pair transition of the 2.76-eV blue band.