Abstract: A new method of broadband constant beamwidth beamforming for arbitrary geometry arrays is proposed in this paper. In the method, the response vector of arbitrary geometry array is expanded in the form of sum of an infinite series, whose core function is. the first kind Bessel function. The high terms of this series are truncated so that the array response vectors at different frequency components were transformed to the reference frequency and the constant beamwidth beamforming vectors are ready to obtain. With these beamforming vectors, the beams at different frequencies are same as the reference beam. A reference beam optimizing method based on adaptive processing is also proposed to optimize the reference beam of arbitrary geometry arrays. Computer simulation for a uniform circular array verified the effectiveness of the new method proposed in this paper.