When the length of the filter and consequently the number of filter coefficients increase, the design of the filter becomes complex and therefore the popular NLMS algorithm has been replaced with MMax NLMS algorithm. But its performance in terms of convergence characteristics reduces to an extent though the filter design becomes very easy i.e., convergence occurs at a later stage taking too much computational time for the processing of the signal. In this paper, a proposal for improving the convergence characteristics is made without compromising the performance of the design and affecting the tap-selection process of the MMax NLMS algorithm. With the introduction of the concept of variable step-size for the filter coefficients, loss in the performance due to MMax NLMS algorithm can be effectively lowered and the convergence is better achieved in the filter deign.