In　this　paper,　we　study　the　k-level　facility　location　problem　with　outliers　(k-LFLPWO),　which　is　an　extension　of　the　well-known　k-level　facility　location　problem　(k-LFLP).　In　the　k-LFLPWO,　we　are　given　k　facility　location　sets,　a　client　location　set　of　cardinality　n　and　a　non-negative　integer　q　＜　n.　Every　facility　location　set　has　a　different　level　which　belongs　to　{1,　2,...,　k}.　For　any　facility　location,　there　is　an　opening　cost.　For　any　two　locations,　there　is　a　connecting　cost.　We　wish　to　connect　at　least　n　-　q　clients　to　opened　facilities　from　level　1　to　level　k,　such　that　the　total　cost　including　opening　costs　and　connecting　costs　is　minimized.　Our　main　contribution　is　to　present　a　6-approximation　algorithm,　which　is　based　on　the　technique　of　primal-dual,　for　the　k-LFLPWO.