Spin resonance of a two-dimensional electron system confined in a GaN/AlGaN heterostructure grown by molecular beam epitaxy was resistively detected over a wide range of magnetic field and microwave frequency. Although the spin-orbit interaction is strong in this type of heterostructure at zero magnetic field, surprisingly the width of the detected spin resonance line was very narrow—down to 6.5 mT at 13.3 T. The spin depolarization time extracted from the resonance linewidth was estimated to be 2 ns. The electron g-factor was measured with high accuracy, resembling a value close to the free-electron value and its dependence on the magnetic field was studied.