Artificial　neural　network　technique　has　gained　recognition　as　a　powerful　technique　in　microwave　modeling　and　design.　This　paper　proposes　a　novel　deep　neural　network　topology　for　parametric　modeling　of　microwave　components.　In　the　proposed　deep　neural　network,　the　outputs　are　S-parameters.　The　inputs　of　the　proposed　model　include　geometrical　variables　and　the　frequency.　We　divide　the　hidden　layers　in　the　proposed　deep　neural　network　topology　into　two　parts.　Hidden　layers　in　Part　I　handle　both　the　geometrical　inputs　and　the　frequency　inputs　while　hidden　layers　in　Part　II　only　handle　the　geometrical　inputs.　In　this　way,　more　training　parameters　are　utilized　to　specifically　learn　the　relationship　between　the　S-parameters　and　the　geometrical　variables,　which　are　more　complicated　than　that　between　the　S-parameters　and　the　frequency.　The　purpose　is　to　reduce　the　total　number　of　training　parameters　in　the　deep　neural　network　model.　New　formulations　are　derived　to　calculate　the　derivatives　of　the　error　function　with　respect　to　training　parameters　in　the　deep　neural　network.　Taking　advantage　of　the　calculated　derivatives,　we　propose　an　advanced　two-stage　training　algorithm　for　the　deep　neural　network.　The　two-stage　training　algorithm　can　determine　the　number　of　hidden　layers　in　both　parts　during　the　training　process　and　guarantee　that　the　proposed　deep　neural　network　model　can　achieve　the　required　model　accuracy.　The　proposed　deep　neural　network　can　achieve　similar　model　accuracy　with　less　training　parameters　compared　to　the　commonly　used　fully　connected　neural　network.　The　proposed　technique　is　demonstrated　by　two　microwave　parametric　modeling　examples.