The　local　community　detection　(LCD)　method　can　discover　the　local　community　structure　in　which　the　seed　node　is　located.　Compared　with　global　community　detection,　local　community　detection　is　characterized　by　its　low　cost　and　high　efficiency.　However,　most　existing　LCD　methods　only　return　a　non-overlapping　community.　Individuals　in　the　real　world　may　participate　in　multiple　communities,　which　can　only　be　discovered　by　using　overlapping　local　community　detection　methods.　In　this　study,　an　overlapping　local　community　detection　algorithm　based　on　modularity　and　node　transitivity.　First,　the　scope　and　structure　information　of　the　overlapping　communities　are　obtained　according　to　the　node　transitivity.　Second,　NMF　is　used　to　obtain　the　number　of　overlapping　communities.　Finally,　the　local　modularity　density　based　on　edge　weights　is　used　to　refine　the　detected　local　communities.　The　experimental　results　validate　the　high　performance　of　our　method　to　the　other　method　in　comparison.　©　2021,　Springer　Nature　Singapore　Pte　Ltd.