In this paper, a direct frequency domain approximation method of wavelet filter was proposed based on the beetle antennae search algorithm (BAS), aiming at the problems of less methods to construct wavelet filter in frequency domain, no guarantee of filter stability and low approximation accuracy. Firstly, the approximation rational formula was designed according to the basic requirements of the wavelet filter circuit. Then, based on the rational formula, a frequency domain optimization model of wavelet filter approximation was established considering the constraint conditions of filter circuit stability, positive reality and zero initial value. Finally, Gaussian and Marr wavelet were taken as examples, in which the BAS algorithm was used to solve the optimization mathematical model to obtain rational parameters. The approximation results are compared with other frequencydomain methods in time and frequency domain. The simulation and calculation results show that the proposed approach has a good approximation effect under the same conditions. The mean square errors (MSE) of the fifthorder Gaussian wavelet and seventhorder Marr wavelet are only 3446 8×10-4 and 7346 2×10-4 respectively.