Correlation　clustering　problem　is　an　elegant　clustering　problem　and　has　many　applications　in　protein　interaction　networks,　cross-lingual　link　detection,　etc.　In　this　paper,　we　introduce　the　capacitated　correlation　clustering　problem　with　penalties　by　combining　the　capacitated　correlation　clustering　problem　and　the　correlation　problem　with　penalties.　There　are　two　main　contributions　in　this　paper.　The　first　one　is　that　we　give　an　integer　programming　for　the　capacitated　correlation　clustering　problem　with　penalties.　The　second　one　is　that　we　provide　an　LP-based　(4　/　(4　-　5　α),　8　/　α)　-bi-criteria　approximation　algorithm　for　this　problem,　where　parameter　α∈　(0,　4　/　9　].　©　2021,　Springer　Nature　Switzerland　AG.