To　learn　Bayesian　Network　(BN)　structure　from　incomplete　data,　this　paper　proposed　an　approach　combined　with　both　processes　of　data　completing　and　Ant　Colony　Optimization　(ACO).　First,　unobserved　data　are　randomly　initialized,　thus　a　complete　data　is　got.　Based　on　such　a　data　set,　an　initialization　BN　is　learned　by　Ant　Colony　Algorithm.　Second,　in　light　of　the　current　best　structure　of　evolutionary　process,　Expectation　Maximization　(EM)　estimating　and　randomly　sampling　are　performed　to　complete　the　data.　Third,　on　the　basis　of　the　new　complete　data　set,　the　BN　structure　is　evolved　by　an　improved　ACO　process.　Finally,　the　second　and　third　steps　are　iterated　until　the　global　best　structure　is　obtained.　Experimental　results　show　the　approach　can　effectively　learn　BN　structure　form　incomplete　data,　and　is　more　accurate　than　MS-EM,　EGA,　BN-GS　algorithms.