Density　functional　theory　calculations　have　been　performed　to　study　the　reaction　mechanism　of　N-2　thermal　reduction　(N2TR)　over　a　single　metal　atom　incorporated　nitrogen-doped　graphene.　Our　results　reveal　that　the　type　of　metal　atoms　and　their　coordination　environments　have　a　significant　effect　on　the　catalytic　activity　of　N2TR.　Regarding　CoN4-　and　FeN4-embedded　graphene　sheets　that　the　metal　atom　is　fourfold　coordinated,　they　are　inactive　for　N2TR　owing　to　the　poor　stability　of　the　adsorbed　H-2　and　N-2　molecules.　In　contrast,　if　the　monodisperse　metal　atom　is　surrounded　by　three　N　atoms,　namely,　CoN3/G　and　FeN3/G　show　activity　toward　N2TR,　and　catalytic　conversion　of　N-2　into　ammonia　is　achieved　through　the　associative　mechanism　rather　than　the　dissociative　mechanism.　Further　investigations　show　that　the　synthesis　of　NH3　over　the　two　surfaces　is　mainly　through　the　formation　of　an　NHNH*　intermediate;　however,　the　detailed　reaction　mechanisms　are　sensitive　to　the　type　of　metal　atom　introduced　into　N-doped　graphene.　Based　on　the　calculated　kinetic　barriers,　FeN3/G　exhibits　a　better　catalytic　activity　for　N2TR.　The　superior　performance　of　FeN3/G　can　be　attributed　to　the　fact　that　this　surface　prefers　a　high　spin-polarized　state　during　the　whole　process　of　N2TR,　while　the　non-spin　polarized　state　is　predicted　as　the　ground　state　for　most　of　the　elementary　steps　of　N-2-fixation　over　CoN3/G.　The　present　study　provides　theoretical　insights　into　developing　graphene-based　single　atom　catalysts　with　a　high　activity　toward　ammonia　synthesis　through　N2TR.