The performance of Capon beamformer degrades sharply in the presence of array steering vector mismatch. To solve this problem, a robust beamforming algorithm based on semi-definite programming and rank-one decomposition is proposed, which improves the robustness of the adaptive beamforming by estimating an actual steering vector. The constraints for estimating the steering vector are deduced under the requirement that the estimate does not weaken the ability to suppress interference and noise, and the analysis shows that the approach to formulating constraint using matrix pre-filter is reasonable. The optimization problem is constructed and converted into a semi-definite relaxation problem, and rank-one decomposition technique is adopted in order to obtain the optimal solution. The simulation results demonstrate that compared with the existing algorithms, the proposed algorithm offers high SINR (signal to interference plus noise power ratio) and accuracy of power estimation, with the sole prior information about the angular vector in which the actual signal lies.