In this work, we propose a low-complexity robust adaptive beamforming (RAB) technique which estimates the steering vector using a Low-Complexity Shrinkage-Based Mismatch Estimation (LOCSME) algorithm. The proposed LOCSME algorithm estimates the covariance matrix of the input data and the interference-plus-noise covariance (INC) matrix by using the Oracle Approximating Shrinkage (OAS) method. LOCSME only requires prior knowledge of the angular sector in which the actual steering vector is located and the antenna array geometry. LOCSME does not require a costly optimization algorithm and does not need to know extra information from the interferers, which avoids direction finding for all interferers. Simulations show that LOCSME outperforms previously reported RAB algorithms and has a performance very close to the optimum.