In this paper, we address a beamforming application based on the capture of far-field speech data from a single speaker in a real meeting room. After the position of the speaker is estimated by a speaker tracking system, we construct a subband-domain beamformer in generalized sidelobe canceller (GSC) configuration. In contrast to conventional practice, we then optimize the active weight vectors of the GSC so as to obtain an output signal with maximum negentropy (MN). This implies the beamformer output should be as non-Gaussian as possible. For calculating negentropy, we consider the Γ and the generalized Gaussian (GG) pdfs. After MN beamforming, Zelinski post- filtering is performed to further enhance the speech by remov- ing residual noise. Our beamforming algorithm can suppress noise and reverberation without the signal cancellation problems encountered in the conventional beamforming algorithms. We demonstrate this fact through a set of acoustic simulations. More- over, we show the effectiveness of our proposed technique through a series of far-field automatic speech recognition experiments on the Multi-Channel Wall Street Journal Audio Visual Corpus (MC- WSJ-AV), a corpus of data captured with real far-field sensors, in a realistic acoustic environment, and spoken by real speakers. On the MC-WSJ-AV evaluation data, the delay-and-sum beamformer with post-filtering achieved a word error rate (WER) of 16.5%. MN beamforming with the Γ pdf achieved a 15.8% WER, which was further reduced to 13.2% with the GG pdf, whereas the simple delay-and-sum beamformer provided a WER of 17.8%. To the best of our knowledge, no lower error rates at present have been reported in the literature on this ASR task.