Deep neural network is now a new trend towards solving different problems in speech processing. In this paper, we propose a discriminative deep recurrent neural network (DRNN) model for monaural speech separation. Our idea is to construct DRNN as a regression model to discover the deep structure and regularity for signal reconstruction from a mixture of two source spectra. To reinforce the discrimination capability between two separated spectra, we estimate DRNN separation parameters by minimizing an integrated objective function which consists of two measurements. One is the within-source reconstruction errors due to the individual source spectra while the other conveys the discrimination information which preserves the mutual difference between two source spectra during the supervised training procedure. This discrimination information acts as a kind of regularization so as to maintain between-source separation in monaural source separation. In the experiments, we demonstrate the effectiveness of the proposed method for speech separation compared with the other methods.