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.