In adaptive beamforming, the presence of the desired signal component in the training data, small sample size, and imprecise knowledge of the desired signal steering vector are the main causes of performance degradation. In order to solve this problem, this paper proposed a robust adaptive beamforming algorithm which performed interference-plus-noise covariance matrix reconstruction and desired signal steering vector estimation. In this algorithm, first the interference-plus-noise covariance matrix was reconstructed using Multiple Signal Classification (MUSIC) spatial spectrum in the signal-free angle section, then the constraint that prevented the convergence of the estimate of the desired signal steering vector to any of the interference steering vectors or their linear combination was derived, next this constraint was used together with the maximization of the array output power to formulate an optimization problem of estimating the desired signal steering vector, and convex optimization software was used to yield the desired signal steering vector. In the paper, the computational complexity of the proposed method was discussed and its effectiveness and superiority were validated by simulations. The simulation results demonstrate that the Signal to Interference plus Noise Ratio (SINR) of proposed adaptive beamformer is almost always close to optimal in a very large range of Signal-to-Noise Ratio (SNR) in the scenarios of random signal and interference look direction mismatch and incoherent local scattering, which is more robust than the existing beamformers.