Adaptive beamforming methods will be degraded sharply in the presence of steering vector errors. The design methods of robust adaptive beamforming become more flexible when the convex optimization technique is used. However, this leads to high computational-complexity and more difficulties for engineering applications. To solve these problems, a robust adaptive beamforming based on the least square estimation is proposed, and a laconic solution method using one-dimensional search is derived. The standard Capon beamformer (SCB) is converted to a robust least-square problem based on the principle of generalized sidelobe canceller, and is then changed into a problem of second-order program. In order to reduce the amount of computation, a one-dimensional search method is deduced using the relationship between the primal and dual problems of second-order program, and Newton iteration method is adopted to obtain the optimal solution. The computational complexity of the proposed algorithm is in the same order of magnitude as that of the SCB. Simulation results demonstrate the robustness of the proposed algorithm in the case of steering vector mismatch and snapshot deficiency.