In performing blind deconvolution to remove reverberation from speech signal, most acoustic deconvolution filters need a great many number of taps, and acoustic environments are often time-varying. Therefore, deconvolution filter coefficients should find their desired values with limited data, but conventional methods need lots of data to converge the coefficients. In this paper, we use sparse priors on the acoustic deconvolution filters to speed up the convergence and obtain better performance. In order to derive a learning algorithm which includes priors on the deconvolution filters, we discuss that a deconvolution algorithm can be obtained by the joint probability density of observed signal and the algorithm includes prior information through the posterior probability density. Simulation results show that sparseness on the acoustic deconvolution filters can be successfully used for adaptation of the filters by improving convergence and performance.