The maximum a posteriori estimator based on HMM’s is successful to some degree because of the incorporation of prior knowledge of speech and markovian properties of the models. The enhanced speech quality is, however, not satisfying at low input SNR. In order to improve speech quality at low input SNR, this paper proposes a method that incorporates codebook constrained Wiener filter into MAP framework to impose spectral constraints on estimated speech signals. The objective measures, global SNR and Itakura-Saito distortion measure, verified the quality improvement of the proposed method.