Compared　to　global　community　detection,　local　community　detection　aims　to　find　communities　that　contain　a　given　node.　Therefore,　it　can　be　regarded　as　a　specific　and　personalized　community　detection　task.　Local　community　detection　algorithms　based　on　modularity　are　widely　studied　and　applied　because　of　their　concise　strategies　and　prominent　effects.　However,　they　also　face　challenges,　such　as　sensitivity　to　seed　node　selection　and　unstable　communities.　In　this　paper,　a　local　community　detection　algorithm　based　on　local　modularity　density　is　proposed.　The　algorithm　divides　the　formation　process　of　local　communities　into　a　core　area　detection　stage　and　a　local　community　extension　stage　according　to　community　tightness　based　on　the　Jaccard　coefficient.　In　the　core　area　detection　stage,　the　modularity　density　is　used　to　ensure　the　quality　of　the　communities.　In　the　local　community　extension　stage,　the　influence　of　nodes　and　the　similarity　between　the　nodes　and　the　local　community　are　utilized　to　determine　boundary　nodes　to　reduce　the　sensitivity　to　seed　node　selection.　Experimental　results　on　real　and　artificial　networks　demonstrated　that　the　proposed　algorithm　can　detect　local　communities　with　high　accuracy　and　stability.　©　2021,　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.