The　green　direct　propylene　(C3H6)　epoxidation　on　MoO(x)is　well　studied　by　experimental　methods.　However,　the　detailed　molecular　reaction　mechanism　studies　using　the　theoretical　study　method　are　few.　Here,　the　different　oxidation　heterogeneous-homogeneous　pathways　for　MoOx/SiO(2)catalyst　are　calculated,　mainly　involving　Mo=O　on　di-oxo　tetracoordinate　MoOx,　allyl　peroxy　(C3H5OO　center　dot),　and　allyloxy　(C3H5O　center　dot)　radicals.　The　results　show　that,　for　surface　reaction　mechanism　with　Mo=O,　the　barriers　of　propylene　oxide　(PO)　and　acetone　generation　are　too　high;　in　comparison,　the　byproduct　acrolein　is　more　beneficial　product　with　a　lower　barrier.　In　heterogeneous-homogeneous　pathways,　the　desorbed　allyl　(C3H5　center　dot)　from　the　surface　can　easily　combine　with　O(2)to　synthesize　C3H5OO　center　dot　radical,　and　in　the　partial　oxidation　of　propylene　with　C3H5OO　center　dot　as　an　oxidant,　PO　is　more　beneficial　with　a　low　barrier　compared　to　byproducts　such　as　propanal,　acetone,　acetaldehyde,　etc.　These　indicate　that　(a)　gas-phase　free　radical　reactions　have　important　effects　on　PO　generation,　in　which　C3H5OO　center　dot　is　the　main　active　species;　(b)　on　MoO(x)surface,　Mo=O　is　difficult　to　be　used　as　the　active　O　species　for　PO　production.　Further　research　is　needed　on　other　active　sites　such　as　Mo-O-Mo　or　defective　sites.