Traditional adaptive beamformers are sensitive to model mismatch and they have poor performances when the input signal-to-noise ratio (SNR) is close to or more than interference-to-noise ratio (INR). In this letter, a novel robust adaptive beamforming (RAB) algorithm based on twice interference-plus-noise covariance (INC) matrix reconstruction is proposed. Firstly, the desired signal (DS) steering vector is estimated by the alternating projection algorithm based on the antenna array geometry and angular sector prior information. Then, the proposed method obtains the eigenvalue corresponding to DS by correlation coefficient and takes the place of it by noise power to obtain the first INC matrix. Furthermore, the second precise covariance matrix is reconstructed based on the theoretical INC matrix expression. The interferences powers are estimated by the theoretical formulation of the interference covariance matrix (ICM), which is derived from the first INC matrix. The simulation results demonstrate that the proposed algorithm achieves good performance especially when the input SNR is high, and its performance is close to the optimal beamformer in the case of look direction error.