Multi-label　propagation　algorithms　(MLPAs)　have　nearly　linear　time　complexity,　but　the　accuracy　and　stability　still　need　to　be　improved　when　applied　to　overlapping　community　discovery.　Inspired　from　the　idea　that　boundary　nodes　are　more　probable　to　appear　in　the　overlapping　regions　of　different　communities,　a　Hierarchical　Multi-label　Propagation　Algorithm　(HMPA)　based　on　node　hierarchy　and　label　propagation　gain　for　overlapping　community　discovery　in　social　networks　is　proposed　in　this　paper.　HMPA　consists　of　three　stages.　Firstly,　HMPA　utilizes　LPAm　to　unfold　initial　non-overlapping　communities.　Secondly,　a　PageRank-like　method　is　proposed　to　mark　the　hierarchy　of　each　node　according　to　the　initial　partition　of　the　first　stage.　Finally,　multi-label　propagation　algorithm　considering　label　propagation　gain　between　nodes,　which　is　calculated　based　on　node　hierarchy,　is　introduced　to　refine　overlapping　region.　Experimental　results　on　both　the　synthetic　and　real　world　networks　show　that　the　proposed　algorithm　can　effectively　solve　the　problems　of　traditional　multi-label　propagation　algorithms　in　terms　of　accuracy　and　stability.