In order to solve the performance degradation of conventional beamformer algorithm under the background of heavy-tailed impulsive noises, a new beamforming approach to combat the arbitrary unknown heavy-tailed impulsive noises of unknown statistics is presented. The new approach, named by Normalized Linearly Constrained Orthogonal Projection (NLCOP) algorithm, is formulated to minimize the noise power of the beamformer's output subject to a pre-specified set of linear constraints. For improving the performance of the beamformer under the background of heavy-tailed impulsive noise of unknown statistics, the new algorithm puts the weighting vector to the noise subspace after the input signal being infinity norm snapshot normalized which makes the second-order-statistics of the input signal existence and bounded. This proposed algorithm does not need prior information or estimation of the impulsive noise's effective characteristic exponent's numerical value, and offers lower sidelobe and better interference-rejection. Simulation results show the effectiveness of the proposed algorithm.