In　this　paper,　we　present　a　novel　approach　for　speech　enhancement　based　on　nonnegative　matrix　factorization　(NMF)　with　the　speech　magnitude　spectrum　constrained　by　a　codebook.　First,　we　utilize　a　codebook　to　model　the　magnitude　spectrum　of　clean　speech　and　a　speech　magnitude　spectrum　codebook　is　trained　containing　the　priori　information　of　speech.　Second,　a　classic　noise　estimation　algorithm　is　employed　to　estimate　the　power　spectral　density　(PSD)　of　noise　to　avoid　noise　classification.　Then,　we　obtain　the　basis　matrix　of　the　noisy　speech　by　combining　the　noise　spectral　with　the　optimal　entry　from　the　speech　codebook.　The　magnitude　spectrum　of　the　noisy　speech　is　decomposed　by　performing　NMF　and　the　estimated　speech　and　noise　components　are　obtained.　Finally,　the　obtained　speech　and　noise　components　are　used　to　enhance　the　noisy　speech.　Moreover,　the　residual　noise　is　further　eliminated　by　applying　the　speech　presence　probability　(SPP).　The　objective　evaluations　demonstrate　that　the　proposed　algorithm　outperforms　the　conventional　NMF　based　method　for　all　the　evaluated　noise　types　at　various　input　signal-to-noise　ratios.