An adaptive beamforming algorithm, which is very robust against look direction mismatch, is proposed in this paper. The essence of the proposed algorithm is to near-perfectly reconstruct the interference-plus-noise covariance matrix using the eigenvalue decomposition, Capon spectrum estimation, and spatial integration, respectively. Theoretical analysis and simulation results show that the steering angle of the proposed beamformer can be self-steered to the desired signal direction whether in large or small look direction deviations. Hence, its performance is almost always close to the optimal value across a wide range of observations as well as a large range of signal-to-noise ratios.