Abstract: Adaptive speech dereverberation is an important research topic in modern speech signal processing. The difficulties lie in the nonwhite and nonstationary properties of speech signals and the long impulse responses of rooms. A novel dereverberation algorithm is proposed for singleinput multiple-output (SIMO) reverberant speech signals which are acquired with microphone array. The reverberant speech signals are firstly aligned according to time-delays which is estimated with cross correlation and secondly pre-whitened with a common whitening filter for all channels so as to keep the cross relation of the pre-whitened reverberant speech signals unchanged, a real-time dereverberation approach is lastly developed with cross relation, inverse power method, which is used for the minimum eigenvector solution of a matrix, and Kalman filter. Simulations and experiments show that the proposed approach works well for speech dereverberation in noisy environments.