The essential robust performance has led to advance in speech enhancement research in annoying adverse noise environments. Multi - microphone systems, which have widely commonly installed in almost all speech applications, have shown improvements in comparison with single - channel approach. Nowadays, the use of microphone array (MA) technology has become popular, because MA has the advantage of exploiting the directional spatial diversity toward the speech source while suppressing background noise at the same time. Minimum Variance Distortionless Response (MVDR) beamformer is one of the most useful beamforming techniques for extracting the desired target talker and obtaining the high diversity. Unfortunately, in many speech acoustic devices, such as voice-controlled systems, hearing aids, teleconference systems, mobile phones, the recorded MA signals are often degraded due to surrounding noise, third-party talkers and complex environments. These reasons cause the corrupted speech quality, speech intelligibility and unsatisfactory perceptual for the listener. This paper discusses an effective post-filtering by taking into account the statistics of the MA properties for further removing the remaining noise component. The conducted numerical experiments has shown the effectiveness of the proposed method in reducing noise level to 9.5 dB, increasing the speech quality in the term of the signal-to-noise ratio (SNR) from 7.3 to 10.7 dB. The suggested method can be applied into multi-channel systems in various types of recording scenarios.