The hydrodeoxygenation (HDO) reaction is crucial to the upgrading of biomass-derived furfural to produce a promising fuel additive, 2-methylfuran. In order to enhance the stability of the molybdenum carbide (Mo2C) catalyst, this work utilizes cobalt (Co) modification to tune the oxygen and furfural binding energies on Mo2C. Density functional theory (DFT) calculations of the adsorption configuration of furfural on Mo2C(0001) and cobalt-modified molybdenum carbide (Co/Mo2C(0001)) reveal that the C=O bond of furfural is elongated, facilitating the selective C=O scission to produce 2-methylfuran. The reduced oxygen and furfural binding energies on Co/Mo2C(0001) allow the facile removal of surface oxygen and furfural to improve the stability of the catalyst. Temperature-programmed desorption (TPD) experiments on model surfaces confirm the enhanced stability and overall HDO performance of Co/Mo2C/Mo(110). Based on the results from high-resolution electron energy loss spectroscopy (HREELS), 2-methylfuran-like intermediates are observed on both Mo2C/Mo(110) and Co/Mo2C/Mo(110). Parallel reactor evaluations over the corresponding powder catalysts further demonstrate the enhanced stability of Co/Mo2C over Mo2C at ambient pressure. This work illustrates the important roles of oxygen and furfural binding energies in the furfural HDO reaction on both model surfaces and powder catalysts, which in turn provides insights into designing selective and stable carbide-based catalysts for HDO reactions.