We present a sequential noise compensation method based on the sequential Kullback proximal algorithm, which uses the Kullback-Leibler divergence as a regularization function for the maximum likelihood estimation. The method is implemented as filters. In contrast to sequential noise compensation method based on the sequential EM algorithm, the convergence rate of the method and estimation error after convergence can be adjusted by a relaxation factor, where the sequential EM algorithm corresponds to the particular case of the presented algorithm. Through experiments on parameter estimation and speech recognition in noise, we verified the efficacy of the algorithm.