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Biogas contains more than 40% CO₂ that can be removed to produce high quality CH₄. Recently, CH₄ production from CO₂ methanation has been reported in several studies. In this study, CO₂ methanation of biogas was performed over a 20 wt% Ni-Mg-Al catalyst, and the effects of CO₂ conversion rate and CH₄ selectivity were investigated as a function of CH₄, O₂, H₂O, and N₂ compositions of the biogas. At a gas hourly space velocity (GHSV) of 30,000 h⁻¹, the CO₂ conversion rate was ~79.3% with a CH₄ selectivity of 95%. In addition, the effects of the reaction temperature (200–450 °C), GHSV (21,000–50,000 h⁻¹), and H₂/CO₂ molar ratio (3–5) on the CO₂ conversion rate and CH₄ selectivity over the 20 wt% Ni-Mg-Al catalyst were evaluated. The characteristics of the catalyst were analyzed using Brunauer–Emmett–Teller surface area analysis, X-ray diffraction, X-ray photoelectron spectroscopy, and scanning electron microscopy. The catalyst was stable for approximately 200 h at a GHSV of 30,000 h⁻¹ and a reaction temperature of 350 °C. CO₂ conversion and CH₄ selectivity were maintained at 75% and 93%, respectively, and the catalyst was therefore concluded to exhibit stable activity.