With respect to N-polar (0001) GaN grown on a sapphire substrate, the effects of Mg doping on the surface morphology, and the optical, and electrical properties are precisely investigated. By doping Mg, hillocks observed on the surface of (0001) GaN can be suppressed, while step bunching becomes severe. The atomic terrace width is extended with increasing Mg/Ga precursor ratio. Mg doping can promote the surface migration of Ga adatoms on a GaN surface during growth. In the case of heavily Mg-doped GaN, atomic steps become wavy. From photoluminescence spectra, the dominant transition was found to change from near-band-edge transition to donor-acceptor-pair transition. Hall-effect measurement shows p-type conduction at room temperature for a sample grown with the Mg/Ga precursor ratio of 4.5×10%3. The activation energy is 143 meV, which is comparable to that of Mg in the conventional Ga-polar (0001) GaN.