Aiming at the frequency distortion problem in the design of frequency weighting digital filter based on bilinear transformation, an evolutionary method based on modified Imperialist Competitive Algorithm（MICA）has been proposed to design digital IIR filter. In order to help the algorithm to escape from local minima, the paper introduces a chaotic function to make the search range wider in the assimilation operation of ICA. Meanwhile, a clone evolution operator is introduced in the competition operation, guiding the search for global optimization efficiently. Then, the optimization model of modified ICA of the filter in sound-level meter are designed based on the research of the source of error in IIR filter. The coefficients of frequency weighted are searched based on the MICA. The results of both simulation and application show the performance of the design method to find better solution, indicating that the proposed method can significantly improve the precision and the error can be controlled within the order of 10-3 dB. Finally, the test of Frequency weighting under the different acoustic signal level with noise verifies that the error of the MICA test can be maintained in the order of 10-2 dB. and fully meet the design requirements of sound level meter (Class 1) in the national standard of GB/T 3241-2010.