Ethylene decomposition over Co(0001) surface has been systematically studied by spin-polarized density functional theory calculations aiming to investigate the detail mechanism at the atomic level. All C-H bond and C-C bond scission reactions were computed and all the intermediates were considered. It is concluded that the C-H bond breaking reaction is always advantageous for a species possessing both C-H scission and C-C scission modes. C-2 cluster is practicable formed during ethylene decomposition, which is coincide with experiment results. However, the high activated barrier blocks the C-C bond scission reaction of C-2. After comparative analysis, two pathways of C-2 cluster formation and two pathways of carbon monomer formation were proposed. These results provide novel information on ethylene decomposition over Co(0001), deepening our understanding of relevant catalytic reactions such as the carbon deposition and initial path to graphene formation. [GRAPHICS] .