In view of the problem of adaptive weight mismatch caused by disturbance and steering vector mismatch in traditional beamformers, which leads to sharp decline of algorithm performance and even cancellation of expected signal, a robust beamforming method combining covariance matrix reconstruction and alternating direction method of multipliers (ADMM) was proposed. Firstly, on the basis of the maximum output power criterion of beamformer, an optimization model was designed to solve the optimal steering vector. Then, according to the spatial power spectrum function of the Capon algorithm, the covariance matrix was reconstructed with the defined interference range to widen the null and enhance the anti-motion interference ability of the system. Finally, for the quadratic inequality constraint problem of the steering vector, the essence was to estimate the difference between the steering vector and the expected steering vector. In this method, ADMM was adopted to solve the quadratic programming problem iteratively, and the specific solution of the steering vector in each iteration was obtained. In addition, the complexity of the algorithm was analyzed. Experimental results showed that compared with the existing beamforming algorithms, the proposed method widened the null at the interference point and improved the anti-jamming performance of the beam. Combined with complexity, it was proved that the algorithm was faster than the existing algorithm and could correct the mismatched steering vector well. This paper also provides a way to solve the quadratic inequality constraint problem and improve the performance of beamforming algorithm.