In many applications of sonar systems, broadband beamformer design is one of the most important issues due to its capability of retaining target signatures in the mainbeam region and suppressing noise and interference from sidelobe region. In order to decrease the influences of amplitude and phase errors of the FIR filter for broadband beamforming, the FIR digital filter with rigid linear phase was obtained by linearly constrained minimum variance adaptation algorithm, and an iterative algorithm was used to design approximate equiripple FIR digital filters through adaptively obtaining optimum cost function based on amplitude error function. These improved approaches resulted in the best weights of the FIR filter to reach a best fit between the FIR digital filter response and the design requirements. Results of computer simulation for a 10 element equally spaced line array showed that these algorithms were effective, and can be applied to arbitrary array.