A novel robust adaptive beamforming technique is proposed to solve the problem of performance degradation with one single snapshot. A sparse signal recovery model under the non‐convex optimisation framework is first established, which dispenses with the mismatched sample covariance matrix, an indispensable part of most existing beamformers. Then, an iterative algorithm is designed to solve the optimisation problem by using the p ‐shrinkage operator and the alternating direction method of multipliers. The iteration steps are closed form and convenient to apply in practice. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm.