Non-negative matrix factorization (NMF) is a powerful approach to single channel audio source separation. In a supervised setting, NMF is first applied to train the basis spectra of each sound source. At test time, NMF is applied to the spectrogram of a mixture signal using the pretrained spectra. The source signals can then be separated out using a Wiener filter. A typical way to train the basis spectra of each source is to minimize the objective function of NMF. However, the basis spectra obtained in this way do not ensure that the separated signal will be optimal at test time due to the inconsistency between the objective functions for training and separation (Wiener filtering). To address this, a framework called discriminative NMF (DNMF) has recently been proposed. In in this work a multiplicative update algorithm was proposed for the basis training, however one drawback is that the convergence is not guaranteed. To overcome this drawback, this paper proposes using a majorization-minimization principle to develop a convergence-guaranteed algorithm for DNMF. Experimental results showed that the proposed algorithm outperformed standard NMF and DNMF using a multiplicative update algorithm as regards both the signal-to-distortion and signal-to-interference ratios.