Correlation　clustering　problem　(CorCP)　is　a　classical　clustering　problem,　which　clusters　data　based　on　the　similarity　of　data　set,　and　has　many　applications　in　interaction　networks,　cross-lingual　link　detection,　and　communication　networks,　etc.　In　this　paper,　we　study　a　practical　generalization　of　the　CorCP,　called　the　capacitated　correlation　clustering　problem　(the　capacitated　CorCP),　by　constructing　a　labeled　complete　graph.　On　this　labeled　complete　graph,　each　vertex　represents　a　piece　of　data.　If　two　pieces　of　data　are　similar,　then　the　edge　between　the　corresponding　vertices　is　marked　by　a　positive　label　+.　Otherwise,　this　edge　is　marked　by　a　negative　label　-.　The　objective　of　the　capacitated　CorCP　is　to　group　some　similar　data　sets　into　one　cluster　as　far　as　possible,　while　satisfying　the　cluster　capacity　constraint.　To　achieve　this　objective,　we　shall　partition　the　vertex　set　of　the　labeled　complete　graph　into　several　clusters,　each　cluster＇s　size　subjecting　to　an　upper　bound,　so　as　to　minimize　the　number　of　disagreements.　Here　the　number　of　disagreements　is　defined　as　the　total　number　of　the　edges　with　positive　labels　between　clusters　and　the　edges　with　negative　labels　within　clusters.　Different　with　the　previous　algorithm　in　[18],　which　subjects　to　the　constraint　on　the　cluster　size　by　a　penalty　measure,　we　design　an　algorithm　for　the　capacitated　CorCP　to　directly　output　a　feasible　solution　by　iteratively　constructing　clusters　based　on　a　preset　threshold.　Through　carefully　setting　the　threshold　and　sophisticatedly　analyzing,　our　algorithm　is　proved　to　have　an　improved　approximation　ratio　of　5.37.　In　addition,　we　also　conduct　a　series　of　numerical　experiments　to　demonstrate　the　effectiveness　of　our　algorithm.　　©　2023　World　Scientific　Publishing　Company.