Lower　bounded　correlation　clustering　problem　(LBCorCP)　is　a　new　generalization　of　the　correlation　clustering　problem　(CorCP).　In　the　LBCorCP,　we　are　given　an　integer　L　and　a　complete　labelled　graph.　Each　edge　in　the　graph　is　either　positive　or　negative　based　on　the　similarity　of　its　two　endpoints.　The　goal　is　to　find　a　clustering　of　the　vertices,　each　cluster　contains　at　least　L　vertices,　so　as　to　minimize　the　sum　of　the　number　of　positive　cut　edges　and　negative　uncut　edges.　In　this　paper,　we　first　introduce　the　LBCorCP　and　give　three　algorithms　for　this　problem.　The　first　algorithm　is　a　random　algorithm,　which　is　designed　for　the　instances　of　the　LBCorCP　with　fewer　positive　edges.　The　second　one　is　that　we　let　the　set　V　itself　as　a　cluster　and　prove　that　the　algorithm　works　well　on　two　specially　instances　with　fewer　negative　edges.　The　last　one　is　an　LP-rounding　based　iterative　algorithm,　which　is　also　provided　for　the　instances　with　fewer　negative　edges.　The　above　three　algorithms　can　quickly　solve　some　special　instances　in　polynomial　time　and　obtain　a　smaller　approximation　ratio.　In　addition,　we　conduct　simulations　to　evaluate　the　performance　of　our　algorithms.