In this paper, we propose a method to lower the variance of the coefficients of the LMS-type adaptive filters in the noisy environments. In the method, each coefficient of the adaptive filter is modeled as an random variable with a Gaussian distribution, and its value is estimated as the mean value of the distribution. Besides, when updating each coefficient, we check if the updated value exists within the distribution. We do not update the coefficient value if it exceeds the range of the Gaussian distribution. We describe the theoretical basis of the method, and propose an implementation method which has similar formula as the Gaussian mixture model (GMM) widely used in video, or speech processing. The effectiveness of the proposed method is evaluated by the computer simulations.