An evolutionary algorithm is used to design a finite impulse response digital filter with reduced power consumption. The proposed design approach combines genetic optimization and simulation methodology, to evaluate a multi-objective fitness function which includes both the suitability of the filter transfer function and the transition activity of digital blocks. The proper choice of fitness function and selection criteria allows the genetic algorithm to perform a better search within the design space, thus exploring possible solutions which are not considered in the conventional structured design methodology. Although the evolutionary process is not guaranteed to generate a filter fully compliant to specifications in every run, experimental evidence shows that, when specifications are met, evolved filters are much better than classical designs both in terms of power consumption and in terms of area, while maintaining the same performance.