A speech signal captured by a distant microphone is generally smeared by reverberation, which severely degrades Automatic Speech Recognition (ASR) performance. In this paper, we propose a novel and practical single channel dereverberation scheme, which utilizes the relationship between speech and reverberation. A dereverberation filter derived by the proposed method is capable of efficiently suppressing late reflections, which constitute a major cause of ASR performance degradation. The proposed algorithm can achieve effective dereverberation with a more reasonable computational complexity than conventional methods. Experimental results reveal a substantial improvement in ASR performance even in severely reverberant environments.