This paper presents a fast convergence algorithm for adaptive FIR filters which is a family of the LMS Algorithm.The proposed algorithm controls the step size on the basis of moving average of misadjustment level for a faster convergence. Several additional operations to the LMS operations estimate the misadjustment in the existence of an interference to the misadjustment and average it to provide a stable step size. The new algorithm is applied to adaptive noise cancellation to observe the performance. Computer simulation results showed superior convergence characteristics of the proposed algorithm, improving as much as 90 % over the LMS Algorithm for a multi-tone signal. For a real speech signal, improvent of the new algorithm is degraded but still mom than 50 96 of the LMS convergence time is saved in the simulated case. The acceleration technique of the proposed algorithm is general, thus, could be applied to other algorithms and a variety of applications.