Speech enhancement is fundamental for various real time speech applications and it is a challenging task in the case of a single channel because practically only one data channel is available. We have proposed a supervised single channel speech enhancement algorithm in this paper based on a deep neural network (DNN) and less aggressive Wiener filtering as additional DNN layer. During the training stage the network learns and predicts the magnitude spectrums of the clean and noise signals from input noisy speech acoustic features. Relative spectral transform-perceptual linear prediction (RASTA-PLP) is used in the proposed method to extract the acoustic features at the frame level. Autoregressive moving average (ARMA) filter is applied to smooth the temporal curves of extracted features. The trained network predicts the coefficients to construct a ratio mask based on mean square error (MSE) objective cost function. The less aggressive Wiener filter is placed as an additional layer on the top of a DNN to produce an enhanced magnitude spectrum. Finally, the noisy speech phase is used to reconstruct the enhanced speech. The experimental results demonstrate that the proposed DNN framework with less aggressive Wiener filtering outperforms the competing speech enhancement methods in terms of the speech quality and intelligibility.