Landfilling is the most common waste disposal method adopted all over the world. The degradation of biodegradable fractions of municipal solid waste (MSW) produces methane (CH4) and carbon dioxide (CO2). The migration of these gases into the atmosphere occurs through the cover layer in the landfill. In the present study, the 1D coupled multicomponent transport and the methane oxidation in the landfill covers by methanotrophs of landfill gas (LFG) in landfill covers were simulated using the computational fluid dynamics (CFD) numerical simulation technique. COMSOL Multiphysics_5.6 simulation tool has been used to solve the equations. The simulation has been carried out to simulate the concentration of different gases along the cover's vertical profile and quantify the methane emission from the cover at different parametric values. The numerical model was partially validated with the published data. The parametric study was carried out for different gas generation rates (FCH4), the porosity of cover (e), the maximum oxidation rate (Vmax) and different thicknesses of various cover materials (T) to understand their effects. The results show that methane oxidation efficiency becomes constant after a particular cover thickness. Methane oxidation efficiency decreases with the increase in the FCH4 and decrease in the Vmax. It was also noted that as the porosity increases, the methane oxidation efficiency increases. The developed model can be used to predict methane emissions from landfills.