Adaptive broadband beamforming is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of minimizing the beamformers output power while keeping the distortionless response (DR) in the direction of desired signal and keeping the constant beamwidth (CB) with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming (SOCP). The computer simulations are presented which illustrate the effectiveness of our bearaformer.