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.　©　2015　IEEE.