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The LMS algorithm is commonly used in the optimum design of the adaptive filter, because the LMS adaptive algorithm is a simple algorithm and it can be realized easily. But the convergence behavior and maladjustment of the LMS algorithm is seriously affected by the step-size, and the optimum parameter of step-size cannot be calculated easily. Evolutionary programming is an optimum algorithm in which the optimization of N-dimensions real-numbers are research objects. In this paper, the FIR filter is an example. In the design of the adaptive filter, we use a fast evolutionary programming algorithm. Cauchy mutation takes the place of Gauss mutation for improving the speed of the convergence. This algorithm is not dependent on any parameter; we can get a good result by the simulation and indicate the validity of the algorithm.