The development of CdMgO ternary alloy with a single cubic phase is challenging but meaningful work for technological advancement. In this work, we have grown a series of Cd1−xMgxO ternary random alloys with various Mg concentrations (x = 0, 30, 32, 45, and 55%) on quartz substrate by plasmaassisted molecular beam epitaxy technique. The structural investigations of alloys were performed using the X-ray diffraction technique. The decreases in average crystallite size and lattice parameters were observed with an increase in Mg content in the alloys. X-ray diffraction analysis confirms that a single cubic phase is obtained for alloy compositions. The elemental and morphological studies were carried out using energy-dispersive X-ray spectroscopy and atomic force microscope technique, respectively. The optical investigation was carried out using UV-Vis spectroscopy. The optical bandgaps were estimated using the Tauc relation. The results varied from 2.34 to 3.47 eV by varying the Mg content from zero to 55% in the alloys. The Urbach energy increases from 112 to 350 meV, which suggests a more disordered localized state with an increase in Mg incorporation in the alloys. topics: oxides, ternary alloys, molecular beam epitaxy, Urbach energy