Since a reverberation filter is generally much shorter than the corresponding dereverberation filter, a single-channel speech dereverberation method based on reverberation filter estimation has been developed to improve its performance. Unfortunately, a typical reverberation filter still requires too many coefficients to be accurately estimated using limited speech observations. In order to exploit sparseness of reverberation filter coefficients, in this paper, we present an algorithm to impose a sparse prior to the process of reverberation filter estimation. Simulation results demonstrate that the sparse prior imposition further improves performance of the speech dereverberation method based on reverberation filter estimation.