A　comprehensive　density　functional　theory　calculation　was　employed　to　investigate　the　possible　reaction　pathways　and　mechanisms　of　methane　complete　oxidation　(CH4　+　2O(2)　-＞　CO2　+　2H(2)O)　on　different　manganese　oxides　including　alpha-MnO2(100)　and　beta-MnO2(111)　surfaces.　According　to　a　coupling　of　the　Mars-van　Krevelen　and　Langmuir-Hinshelwood　mechanism,　the　activation　energy　barrier　and　the　reaction　energy　of　each　elementary　surface　reaction　were　determined.　Our　calculated　results　show　that　the　detailed　processes　for　methane　oxidation　on　two　surfaces　are　different　due　to　the　differences　in　the　surface　structure.　The　breaking　of　the　last　C-H　bond　of　CH4　molecule　is　the　rate-determining　step　with　an　activation　barrier　of　0.85　eV　for　alpha-MnO2(100)　surface.　By　contrast,　the　overall　reaction　rate　on　beta-MnO2(111)　surface　is　limited　by　the　dissociation　of　the　second　O-2　molecule　adsorbed　on　the　vacancy　site,　and　re-oxidation　of　the　reduced　beta-MnO2(111)　surface　by　the　gaseous　oxygen　requires　a　much　higher　energy　barrier　of　1.44　eV　As　a　result,　the　alpha-MnO2(100)　exhibits　superior　activity　and　durability　in　the　methane　oxidation　reaction　than　beta-MnO2(111)　surface.　The　present　study　provides　insight　into　understanding　the　structure-catalytic　activity　relationship　of　the　catalysts　based　on　manganese　oxides　towards　the　methane　oxidation　reaction.