This　paper　proposes　a　new　recurrent　neural　network-based　Kalman　filter　for　speech　enhancement,　based　on　a　noise-constrained　least　squares　estimate.　The　parameters　of　speech　signal　modeled　as　autoregressive　process　are　first　estimated　by　using　the　proposed　recurrent　neural　network　and　the　speech　signal　is　then　recovered　from　Kalman　filtering.　The　proposed　recurrent　neural　network　is　globally　asymptomatically　stable　to　the　noise-constrained　estimate.　Because　the　noise-constrained　estimate　has　a　robust　performance　against　non-Gaussian　noise,　the　proposed　recurrent　neural　network-based　speech　enhancement　algorithm　can　minimize　the　estimation　error　of　Kalman　filter　parameters　in　non-Gaussian　noise.　Furthermore,　having　a　low-dimensional　model　feature,　the　proposed　neural　network-based　speech　enhancement　algorithm　has　a　much　faster　speed　than　two　existing　recurrent　neural　networks-based　speech　enhancement　algorithms.　Simulation　results　show　that　the　proposed　recurrent　neural　network-based　speech　enhancement　algorithm　can　produce　a　good　performance　with　fast　computation　and　noise　reduction.　©　2015　Elsevier　Ltd.