Locality　preserving　projection　(LPP)　is　a　dimensionality　reduction　algorithm　preserving　the　neighhorhood　graph　structure　of　data.　However,　the　conventional　LPP　is　sensitive　to　outliers　existing　in　data.　This　article　proposes　a　novel　low-rank　LPP　model　called　LR-LPP.　In　this　new　model,　original　data　are　decomposed　into　the　clean　intrinsic　component　and　noise　component.　Then　the　projective　matrix　is　learned　based　on　the　clean　intrinsic　component　which　is　encoded　in　low-rank　features.　The　noise　component　is　constrained　by　the　l(1)-norm　which　is　more　robust　to　outliers.　Finally,　LR-LPP　model　is　extended　to　LR-FLPP　in　which　low-dimensional　feature　is　measured　by　F-norm.　LR-FLPP　will　reduce　aggregated　error　and　weaken　the　effect　of　outliers,　which　will　make　the　proposed　LR-FLPP　even　more　robust　for　outliers.　The　experimental　results　on　public　image　databases　demonstrate　the　effectiveness　of　the　proposed　LR-LPP　and　LR-FLPP.