In this paper, we propose low-complexity robust adaptive beamforming (RAB) techniques that based on shrinkage methods. The only prior knowledge required by the proposed algorithms are the angular sector in which the actual steering vector is located and the antenna array geometry. We firstly present a Low-Complexity Shrinkage-Based Mismatch Estimation (LOCSME) algorithm to estimate the desired signal steering vector mismatch, in which the interference-plus-noise covariance (INC) matrix is estimated with Oracle Approximating Shrinkage (OAS) method and the weights are computed with matrix inversions. We then develop low-cost stochastic gradient (SG) recursions to estimate the INC matrix and update the beamforming weights, resulting in the proposed LOCSME-SG algorithm. Simulation results show that both LOCSME and LOCSME-SG achieve very good output signal-to-interference-plus-noise ratio (SINR) compared to previously reported adaptive RAB algorithms.