Indoor　localization　has　attracted　more　and　more　attention　because　of　its　importance　in　many　applications.　One　of　the　most　popular　techniques　for　indoor　localization　is　the　received　signal　strength　indicator　(RSSI)　based　fingerprinting　approach.　Since　RSSI　values　are　very　complicated　and　noisy,　conventional　machine　learning　algorithms　often　suffer　from　limited　performance.　Recently　developed　deep　learning　algorithms　have　been　shown　to　be　powerful　for　the　analysis　of　complex　data.　In　this　paper,　we　propose　a　local　feature-based　deep　long　short-term　memory　(LF-DLSTM)　approach　for　WiFi　fingerprinting　indoor　localization.　The　local　feature　extractor　attempts　to　reduce　the　noise　effect　and　extract　robust　local　features.　The　DLSTM　network　is　able　to　encode　temporal　dependencies　and　learn　high-level　representations　for　the　extracted　sequential　local　features.　Real　experiments　have　been　conducted　in　two　different　environments,　i.e.,　a　research　lab　and　an　office.　We　also　compare　the　proposed　approach　with　some　state-of-the-art　methods　for　indoor　localization.　The　results　show　that　the　proposed　approach　achieves　the　best　localization　performance　with　mean　localization　errors　of　1.48　and　1.75　m　under　the　research　lab　and　office　environments,　respectively.　The　improvements　of　our　proposed　approach　over　the　state-of-the-art　methods　range　from18.98%　to　53.46%.