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In this paper, a robust linear programming beamformer (RLPB) is proposed for non-Gaussian signals in the presence of steering vector uncertainties. Unlike most of the existing beamforming techniques based on the minimum variance criterion, the proposed RLPB minimizes the ℓ _∞ -norm of the output to exploit the non-Gaussianity. We make use of a new definition of the ℓ _p -norm (1 ≤ p ≤ ∞) of a complex-valued vector, which is based on the lp-modulus of complex numbers. To achieve robustness against steering vector mismatch, the proposed method constrains the ℓ _∞ -modulus of the response of any steering vector within a specified uncertainty set to exceed unity. The uncertainty set is modeled as a rhombus, which differs from the spherical or ellipsoidal uncertainty region widely adopted in the literature. The resulting optimization problem is cast as a linear programming and hence can be solved efficiently …