Abstract: When an arbitrary unknown signal steering vector mismatch occurs or the training sample size is small, the performance of standard Capon beamforming (SCB) will be severely degraded. The existing algorithms are mostly made for the steering vector errors, with little considering the situations of small training sample size. In this paper, we develop a new approach, which is called vector optimization robust beamforming (VORB), to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch and small training sample size. Our approach is based on the vector optimization concept. It is shown that the proposed algorithm can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently using the well-established optimization tool, Sedumi. It is also shown that the proposed technique can be interpreted in terms of diagonal loading, and how the optimization value of the diagonal loading is affected by different factors. Theory analysis and computer simulations show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms: under different snapshots, SNRs and steering vector uncertainties, VORB can improve the output SINRs about 5 dB; under certain conditions, VORB has sharper spectrum peaks and lower sidelobe level (below -15 dB). Finally, experimental results show that when VORB is applied to the spatial spectrum estimation in practical engineering, the robust high-resolution bearing estimation results can be obtained.