In　most　of　the　existing　LLE　(Local　Linear　Embedding)　based　face　hallucination　methods,　a　LR　(Low　Resolution)　face　image　is　usually　represented　as　a　linear　combination　of　training　samples.　The　combination　coefficients　of　LR　image　are　then　directly　used　to　estimate　the　HR　(High　Resolution)　image.　However,　due　to　the　one-to-many　mapping　from　LR　to　HR　face　space,　the　LR-LLE　coefficients　are　not　as　the　same　as　the　corresponding　HR-LLE　coefficients.　Therefore,　the　estimated　HR　faces　are　different　from　the　ground　truth.　A　novel　face　super-resolution(SR,　also　named　face　hallucination)　method　is　proposed　in　this　paper,　in　which　a　HR-LLE　coefficients　constraint　is　introduced　to　predict　the　coefficients　of　HR　image.　It　can　effectively　reduce　the　error　of　the　estimated　HR-LLE　coefficients.　Then,　we　develop　a　novel　method　to　perform　face　hallucination　based　on　both　the　global　and　local　features.　Experimental　results　show　that　the　proposed　method　provides　improved　performance　over　the　compared　methods　in　terms　of　both　the　subjective　and　objective　quality.