A series of bimetallic catalysts containing nickel supported over MgO–ZrO2 were tested for activity in the dry reforming of carbon dioxide. A nickel–cobalt bimetallic catalyst gave the best performance in terms of conversion and coke resistance from a range of Ni–X bimetallic catalysts, XCa, K, Ba, La, and Ce. The nitrogen-adsorption and hydrogen-chemisorption studies showed the Ni–Co bimetallic supported catalyst to have good surface area with high metal dispersion. This contributed to the high catalytic activity, in terms of conversion activity and stability of the catalyst, at an equimolar methane/carbon dioxide feed ratio. The kinetics of methane dry reforming are studied in a fixed-bed reactor over an Ni–Co bimetallic catalyst in the temperature range 700–800 °C by varying the partial pressures of CH4 and CO2. The experimental data were analyzed based on the proposed reaction mechanism using the Langmuir–Hinshelwood kinetic model. The activation energies for methane and carbon dioxide consumption were estimated at 52.9 and 48.1 kJ mol−1, respectively. The lower value of CO2 activation energy compared to the activation energy of CH4 indicated a higher reaction rate of CO2, which owes to the strong basicity of nanocrystalline support, MgO–ZrO2.