Codebook-based　speech　enhancement　approach　is　an　effective　method　for　reducing　non-stationary　noise.　In　view　of　the　inaccurate　problem　of　estimating　the　short-term　predictor　parameters　of　the　speech　and　noise,　this　paper　proposes　a　codebook-based　maximum　posteriori　probability　(MAP)　speech　enhancement　approach　by　combining　MAP　estimation　and　codebook-based　method.　Based　on　the　prior　information　and　inter-frame　correlation　of　the　short-term　predictor　parameters,　the　paper　develops　both　memoryless　and　memory-based　MAP　predictor　parameters　estimators　which　optimally　get　the　spectral　shapes　and　the　corresponding　excitation　variances.　In　order　to　further　improve　the　accuracy　of　the　parameters,　a　novel　approach　of　estimating　the　excitation　variances　is　proposed　for　the　memory　based　case.　Experimental　results　show　that,　in　comparison　with　the　reference　method,　the　proposed　method　can　get　better　performance　under　various　noise　conditions.