In　this　paper,　we　consider　an　extension　of　the　classical　facility　location　problem,　namely　k-facility　location　problem　with　linear　penalties.　In　contrast　to　the　classical　facility　location　problem,　this　problem　opens　no　more　than　k　facilities　and　pays　a　penalty　cost　for　any　non-served　client.　We　present　a　local　search　algorithm　for　this　problem　with　a　similar　but　more　technical　analysis　due　to　the　extra　penalty　cost,　compared　to　that　in　Zhang　(Theoretical　Computer　Science　384:126-135,　2007).　We　show　that　the　approximation　ratio　of　the　local　search　algorithm　is　,　where　is　a　parameter　of　the　algorithm　and　is　a　positive　number.