Bayesian　network　(BN)　is　one　of　the　most　important　theoretical　models　for　uncertainty　knowledge　expression　and　reasoning.　So　far,　many　BN　structure　learning　algorithms　have　been　proposed.　In　this　paper,　a　fast　algorithm　FI-B&B-MDL　is　developed,　which　considerably　speeds　up　the　original　I-B&B-MDL　algorithm.　Unlike　I-B&B-MDL,　the　new　FI-B&B-MDL　first　uses　only　order-0　and　a　small　number　of　order-1　independence　tests　to　obtain　an　original　structure　graph　so　that　the　number　of　independence　tests　and　database　passes　can　be　decreased,　and　then　takes　mutual　information　between　nodes　as　the　heuristic　knowledge　to　lead　MDL　searches　so　that　the　cut-offs　of　B&B　search　trees　can　be　increased,　and　consequently　the　search　process　is　accelerated.　Experimental　results　show　that　the　new　algorithm　is　effective　and　efficient　in　large　scale　databases,　and　it　is　faster　than　the　original　algorithm.