Cobalt is a potential candidate for replacing copper for interconnects and has been applied in the trenches and vias in the semiconductor industry. A non-oxidizing reactant is required in plasma-enhanced atomic layer deposition (PE-ALD) of thin films of metals to avoid O contamination. PE-ALD of Co has been demonstrated experimentally, but the growth mechanism and key reactions are not clear. In this paper, the reaction mechanism of metal cyclopentadienyl (Cp, C5H5) precursors (CoCp2) and NHx-terminated Co surfaces is studied by density functional theory calculations. The Cp ligands are eliminated by CpH formation via a hydrogen transfer step and desorb from the metal surface. The surface facet plays an important role in the reaction energies and activation barriers. The results show that on the NHx-terminated surfaces corresponding to ALD operating conditions (temperature range 550 K to 650 K), the two Cp ligands are eliminated completely on the Co(100) surface during the metal precursor pulse, resulting in Co atoms deposited on the Co(100) surface. However, the second Cp ligand reaction of hydrogen transfer is thermodynamically unfavorable on the Co(001) surface, resulting in CoCp fragment termination on the Co(001) surface. The final terminations after the metal precursor pulse are 3.03 CoCp/nm2 on the NHx-terminated Co(001) surface and 3.33 Co/nm2 on the NHx-terminated Co(100) surface. These final structures after the metal precursor pulse are essential to model the reaction during the following N-plasma step.