Microphone arrays (MA) based on beamforming have been commonly installed in almost all acoustic devices, commercial equipment, industry products, human–machine interaction, hearing aids, teleconference system, mobile phones. Therefore, speech enhancement is an essential part, which suppresses background noise while recovering the original speech component to achieve an acceptable speech quality, speech intelligibility and perceptual metric listener. MA exploits the a priori information about spatial geometry of MA, the direction of arrival on useful clean speech data, the designed configuration MA, the characteristic of surrounding noise to achieve better noise reduction and speech enhancement at the same time. Adaptive MA are most widely studied in a few decades ago, because of the superiority of tracking acoustical factor, updating the spatial filter’s coefficients for preserving speech component. Generalized Sidelobe Canceller (GSC) beamformer is one of the most effective MA beamforming to extract the desired target speaker at certain direction. However, in a realistic recording scenario, the overall GSC beamformer’s performance often corrupted due to the microphone mismatches, the error of estimating the steering vector, the displacement of MA, the complex and annoying environment. In this article, the author proposed an effective post-filtering for reducing the remaining noise at the output signal of GSC beamformer. The illustrated experiment was conducted in a living room with the existence of incoherent noise, interference and competing talkers. The obtained result has shown the improvement of speech quality in the term of signal-to-noise (SNR) ratio from 11.5 to 12.8 dB and decreased the noise level to 15.1 dB. The perspective simulation has confirmed the advantage of the author’s suggested technique in increasing the speech quality, enhancing the overall GSC beamformer’s performance. The proposed method can be integrated into a multi-channel system for solving more complicated problems.