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.