This　paper　presents　a　codebook-based　speech　enhancement　algorithm　by　using　Markov　process　and　speech-presence　probability　(SPP).　The　Markov　process　is　utilized　to　model　the　correlation　between　the　adjacent　code-vectors　in　the　codebook　for　optimizing　Bayesian　minimum　mean　squared　error　(MMSE)　estimator.　Then　the　proposed　estimator　is　used　to　estimate　spectral　shapes　and　gains　of　speech　and　noise.　The　correlation　between　adjacent　linear　prediction　(LP)　gains　is　also　fully　considered　during　the　procedure　of　parameter　estimation.　Through　the　introduction　of　SPP　in　the　codebookconstrained　Wiener　filter,　the　proposed　Wiener　filter　achieves　the　goal　of　much　more　noise　reduction　and　does　not　result　in　the　speech　component　distortion.　The　evaluation　results　confirm　that　the　proposed　algorithm　has　a　much　better　performance　for　reducing　annoying　background　noise　than　the　conventional　codebook-based　algorithms.