Electon spin resonance measurements have been performed on the Mg-doped wurtzite GaN thin films grown on sapphire substrates by low-pressure metal-organic chemical vapor deposition. The sample set included films as-grown with the regular Mg doped and Mg delta doped samples and the corresponding annealed ones. The resonance signal has been observed from the annealed Mg delta-doped sample with the Lande g value of 2.029. This indicates that the singlet resonance signal originates from the neutral Mg acceptor located at 0.24 eV above the valence band edge and 0.13 eV above the Fermi level because of the nuclear hyperfine spin 1=0 of Mg and the larger value than the free electron g=2.0023.