An efficient approach for the computationtion of the optimum convergence factor is proposed for the LMS algorithm applied to a transversal FIR structure in this study. The approach automatically leads to an optimum step size algorithm at each weight in every iteration that results in a dramatic reduction in terms of convergence time. The algorithm is evaluated in system identification application where two alternative computer simulations are considered for time-invariant and time-varying system cases. The results show that the proposed algorithm needs not appropriate convergence factor and has better performance than AGC(Automatic Gain Control) algorithm and Karni algorithm, which require the convergence factors controlled arbitrarily in computer simulation for time-invariant system and time-varying systems. Also, itis shown that the proposed algorithm has the excellent adaptability campared with NLMS(Normalized LMS) algorithm and RLS (Recursive least Square) algorithm for time-varying circumstances.