This　paper　considers　the　capacitated　correlation　clustering　problem　with　penalties　(CCorCwP),　which　is　a　new　generalization　of　the　correlation　clustering　problem.　In　this　problem,　we　are　given　a　complete　graph,　each　edge　is　either　positive　or　negative.　Moreover,　there　is　an　upper　bound　on　the　number　of　vertices　in　each　cluster,　and　each　vertex　has　a　penalty　cost.　The　goal　is　to　penalize　some　vertices　and　select　a　clustering　of　the　remain　vertices,　so　as　to　minimize　the　sum　of　the　number　of　positive　cut　edges,　the　number　of　negative　non-cut　edges　and　the　penalty　costs.　In　this　paper　we　present　an　integer　programming,　linear　programming　relaxation　and　two　polynomial　time　algorithms　for　the　CCorCwP.　Given　parameter　delta　is　an　element　of　(0,　4/9],　the　first　algorithm　is　a　(8/(4　-　5　delta),　8/delta)-N-criteria　approximation　algorithm　for　the　CCorCPwP,　which　means　that　the　number　of　vertices　in　each　cluster　does　not　exceed　8/(4　-　5　delta)　times　the　upper　bound,　and　the　output　objective　function　value　of　the　algorithm　does　not　exceed　8/delta　times　the　optimal　value.　The　second　one　is　based　on　above　bi-criteria　approximation,　and　we　prove　that　the　second　algorithm　can　achieve　a　constant　approximation　ratio　for　some　special　instances　of　the　CCorCwP.