The　speech　enhancement　is　one　of　the　effective　techniques　to　solve　speech　degraded　by　noise.　In　this　paper　a　fast　speech　enhancement　method　for　noisy　speech　signals　is　presented,　which　is　based　on　improved　Kalman　filtering.　The　conventional　Kalman　filter　algorithm　for　speech　enhancement　needs　to　calculate　the　parameters　of　AR　(auto-regressive)　model,　and　perform　a　lot　of　matrix　operations,　which　usually　is　non-adaptive.　The　speech　enhancement　algorithm　proposed　in　this　paper　eliminates　the　matrix　operations　and　reduces　the　calculating　time　by　only　constantly　updating　the　first　value　of　state　vector　X(n).　We　design　a　coefficient　factor　for　adaptive　filtering,　to　automatically　amend　the　estimation　of　environmental　noise　by　the　observation　data.　Simulation　results　show　that　the　fast　adaptive　algorithm　using　Kalman　filtering　is　effective　for　speech　enhancement.　©　2011　IEEE.