Abstract: FIR (Finite Impulse Response) digital filters are designed using traditional methods such as analog to digital transformation techniques with analog filter topologies like butterworth, chebyshive and elliptic, etc. In addition, it can also be designed by using adaptive algorithms. In this study, FIR arbitrary shape filter can be designed using LMS algorithm. Convergence of the adaptive filter to the optimum weight values depends on the statistical characteristics of the input signal (the correlation matrix Rxx) which is highly depending on the input signal. Maximum step size of the LMS algorithm has been found and the optimum step value is derived based on wiener-hop formula. The proposed algorithm has been theoretically derived, simulated using Matlab and tested for several filter types. The results shown LMS adaptive technique, more flexibility can be achieved in design response for the required filter.