A minimum geometric power distortionless response beamforming approach against impulsive noise (including all α-stable 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.