This　paper　proposes　a　fast　discrete-time　learning　algorithm　for　speech　enhancement　of　single-channel　noisy　speech　signal,　based　on　a　noise　constrained　least　squares　estimate.　Unlike　existing　learning　algorithms　for　the　noise　constrained　estimate,　the　proposed　discrete-time　learning　algorithm　has　a　low　complexity　and　fast　speed.　Simulation　results　show　that　the　proposed　discrete-time　learning　algorithm　has　a　faster　speed　than　the　existing　learning　algorithms　for　speech　enhancement.　Moreover,　the　proposed　discrete-time　learning　algorithm　has　a　good　performance　in　having　a　significant　gain　in　SNR　at　colored　noise.