A minimum geometric power distortionless response beamforming approach against impulsive noise(including all αstable noise) of unknown statistics is proposed.Due to that definite logarithmic moments require no priori knowledge of impulsive noise,this new beamformer substitutes the logarithmic moments for the second-order moments and iteratively minimizes the “geometric power” of the beamformer’s output snapshots,subjected to a linear constraint.Therefore,the proposed beamformer can provide significantly higher output geometric signal-to-noise-andinterference ratio.Moreover,the optimum weight vector is obtained by using a new iteration process.The simulation results prove that the new method is effective. A minimum geometric power distortionless response beamforming approach against impulsive noise (including all αstable noise) of unknown statistics is proposed. Due to that definite logarithmic moments require no priori knowledge of impulsive noise, this new beamformer substitutes the logarithmic moments for the second-order moments and iteratively minimize the “geometric power ” of the beamformer’s output snapshots, subjected to a linear constraint. Beforefore, the proposed beamformer can provide significantly higher output geometric signal-to-noise-andinterference ratio. Moreover, the optimum weight vector is obtained by using a new iteration process. the simulation results prove that the new method is effective.