In　this　paper,　a　novel　deep　neural　network　(DNN)　training　approach　is　proposed　for　speech　enhancement　based　on　nonnegative　matrix　factorization　(NMF)　and　computational　auditory　scene　analysis　(CASA).　Considering　a　higher　correlation　of　NMF　algorithm　along　the　frequency　bins　for　the　time-varying　signals　and　a　high　noise　making　effect　of　CASA,　we　propose　a　new　cost　function　for　DNN　training,　which　consists　of　the　ideal　ratio　mask　(IRM)　and　NMF　based　Wiener-like　filter.　Extensive　experiments　are　carried　out　to　verify　the　performance　of　the　proposed　method.　Moreover,　we　compare　the　performance　of　the　developed　algorithm　with　traditional　NMF　approach,　NMF-based　linear　minimum　mean　square　error　(LMMSE)　filter　approach　and　CASA　method.　Our　results　demonstrate　that　the　proposed　approach　improved　speech　quality　greatly.