This　paper　proposes　a　new　hybrid　structure　and　microwave　modeling　method　that　combines　polynomial　regression　with　batch-normalized　deep　feedforward　neural　network　(BN-DFN)　to　be　used　in　high-dimensional　microwave　circuit　modeling.　Utilizing　the　proposed　BN-DFN　method　results　in　a　remarkably　faster　training　procedure　compared　to　the　conventional　DFN.　In　addition,　the　superiority　of　the　BN-DFN　method　over　DFN　in　terms　of　accuracy　prepares　this　opportunity　to　perform　high-dimensional　microwave　modeling　using　fewer　training　data　in　comparison　with　the　modeling　with　conventional　DFN.　The　results　show　that　a　data　reduction　of　about　40-80%　can　be　achieved　for　microwave　applications　used　in　this　paper　using　the　proposed　method.　Also,　in　this　paper,　a　hybrid　polynomial　regression　BN-DFN　(HPBN-DFN)　is　proposed　to　further　improve　the　accuracy　of　the　proposed　BN-DFN　method.　The　proposed　HPBN-DFN　method　fine-tunes　the　predicted　values　of　the　BN-DFN　by　passing　them　through　a　polynomial　regression　stage　for　increasing　accuracy.　The　proposed　methods　are　verified　through　two　high-dimensional　parameter-extraction　modeling　examples　of　microwave　filters.