Abstract: To solve the performance degradation of beamformer amid heavy-tailed impulsive noises of unknown statistics, a new beamforming approach to combat the arbitrary unknown heavy-tailed impulsive noises of unknown statistics is presented. The new approach, termed as Normalized-Linearly Constrained Eigencanceler (N-LCEC) algorithm, is formulated as one to minimize the noise power of the beamformer’s output subject to a pre-specified set of linear constraints. To improving the performance of the beamformer amid heavy-tailed impulsive noise of unknown statistics, the new algorithm put the weighting vector to the noise subspace after the input signal being infinity norm snapshot normalized which to keep the second-order-statistics of the input signal existing and finite. This new N-LCEC algorithm has these advantages: (1) simpler computationally with a closed-form solution, (2) needing no prior information nor estimation of the impulsive noise’s effective characteristic exponent’s numerical value, (3) applicable to a wider class of heavy-tailed impulsive noises of unknown statistics, and (4) offering better interference-rejection and low sidelobe. Simulation results demonstrate the validity and superiority of the proposed algorithm.