ZnMgO nanowalls were prepared by plasma-assisted molecular beam epitaxy without a catalyst on c-Al2O3 substrate. The obtained nanowalls have preferred orientation along c axis. The nanowalls are about 10 to 20 nm in thickness and about 50 nm in height. Only Zn, Mg, O and Al signals are detected in the nanowalls from the energy dispersive spectroscopy (EDS). The Mg content is about 3% in ZnMgO nanowalls. The room temperature photoluminescence (PL) spectra shows the emission peak of the ZnMgO nanowalls at 3.346 eV. The origin of the ultraviolet emission is discussed with the help of temperature-dependent PL spectra. The ultraviolet emission band is free exiton recombination observed in the low temperature PL spectra (at 81 K). We also observe the free-to-acceptor (FA) emission of the ZnMgO nanowalls. The acceptor binding energy obtained from photoluminescence studies is about 123 meV. The results show that Mg doping leads to an increase of the acceptor binding energy. The possible growth mechanism of the ZnMgO nanowall networks was discussed.