Adaptive　beamforming　and　deconvolution　techniques　have　shown　effectiveness　for　reducing　noise　and　reverberation.　The　minimum　variance　distortionless　response　(MVDR)　beamformer　is　the　most　widely　used　for　adaptive　beamforming,　whereas　multichannel　linear　prediction　(MCLP)　is　an　excellent　approach　for　the　deconvolution.　How　to　solve　the　problem　where　the　noise　and　reverberation　occur　together　is　a　challenging　task.　In　this　paper,　the　MVDR　beamformer　and　MCLP　are　effectively　combined　for　noise　reduction　and　dereverberation.　Especially,　the　MCLP　coefficients　are　estimated　by　the　Kalman　filter　and　the　MVDR　filter　based　on　the　complex　Gaussian　mixture　model　(CGMM)　is　used　to　enhance　the　speech　corrupted　by　the　reverberation　with　the　noise　and　to　estimate　the　power　spectral　density　(PSD)　of　the　target　speech　required　by　the　Kalman　filter,　respectively.　The　final　enhanced　speech　is　obtained　by　the　Kalman　filter.　Furthermore,　a　complexity　reduction　method　with　respect　to　the　Kalman　filter　is　also　proposed　based　on　the　Kronecker　product.　Compared　to　two　advanced　algorithms,　the　integrated　sidelobe　cancellation　and　linear　prediction　(ISCLP)　method　and　the　weighted　prediction　error　(WPE)　method,　which　are　very　effective　for　removing　reverberation,　the　proposed　algorithm　shows　better　performance　and　lower　complexity.