This paper proposes a gradient-based adaptive weighted median (AWM) algorithm. The AWM is a modification of normal LMS, obtained by applying a proposed adaptive weighted median filter on the input signal instead of using (1.1K) filter. The (AWM) algorithm is designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of inputs. Also, we present an analysis of the (AWM) algorithm, we using the threshold decomposition technique that admitting real-valued signals. This threshold decomposition is used to develop LMS algorithm to optimally design the filter's coefficients to obtain our proposed filter, and Results are presented to illustrate the performance of the proposed algorithm and its application in noisy image filtering.