Community　detection　is　an　important　research　direction　in　the　field　of　complex　network　analysis.　It　aims　to　discover　community　structures　in　complex　networks.　Algorithms　based　on　dynamic　distance　mechanism　can　find　stable　communities　with　various　shapes.　However,　they　still　cannot　discover　overlapping　or　outlier　communities.　This　paper　proposes　an　overlapping　community　discovery　algorithm　based　on　coarsening　and　local　overlapping　modularity.　First,　to　reduce　the　running　time,　a　new　equation　for　computing　the　local　overlapping　modularity　increment　is　derived.　This　equation　finds　the　overlapping　communities,　accurately　and　quickly.　Second,　a　new　similarity　measuring　strategy　is　designed　to　reduce　the　number　of　outlier　communities.　The　experiments　on　artificial　and　real　datasets　show　that　the　proposed　algorithm　can　discover　the　overlapping　communities,　accurately　and　efficiently.