The increasing demand for renewable fuels and sustainable products has encouraged growing interest in the development of active and selective catalysts for the conversion of carbon monoxide into desirable products. The Fischer–Tropsch process consists of the reaction of a synthesis gas mixture containing carbon monoxide and hydrogen (syngas), which are polymerized into liquid hydrocarbon chains, often using a cobalt catalyst. Here, first-principles calculations based on the density functional theory (DFT) are used to investigate the reaction mechanism of the Fischer–Tropsch synthesis over the Co (001) surface. The most energetically favorable adsorption configurations of the species involved in the carbon monoxide hydrogenation process are identified, and the possible elementary steps of hydrogenation and their related transition states are explored using the Vienna Ab initio simulation package (VASP). The results provide the mechanisms for the formation of CH4, CH3OH and C2H2 compounds, where the calculations suggest that CH4 is the dominant product. Findings from the reaction energies reveal that the preferred mechanism for the hydrogenation of carbon monoxide is through HCO and cis-HCOH, and the largest exothermic reaction energy in the CH4 formation pathway is released during the hydrogenation of cis-HCOH (−0.773 eV). An analysis of the kinetics of the hydrogenation reactions indicates that the CH production from cis-HCOH has the lowest energy barrier of just 0.066 eV, and the hydrogenation of CO to COH, with the largest energy barrier of 1.804 eV, is the least favored reaction kinetically.