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A speech signal captured by a distant microphone is generally contaminated by reverberation and background noise, which severely degrade the automatic speech recognition (ASR) performance. In this paper, we first extend a previously proposed single channel dereverberation algorithm to a multi-channel scenario. The method estimates late reflections using multi-channel multi-step linear prediction, and then suppresses them in the power spectral domain. Second, we analyze the effect of additive noise on the proposed method and provide one solution to the noisy reverberant environment. Experimental results show that the proposed method achieves good dereverberation in noisy reverberant environments, and can significantly improve the ASR performance to that obtained for a non-reverberant environment.