Abstract: Under the circumstances of multipath propagation, the performances of existing adaptive array algorithms are known to degrade substantially in the presence of even slighter mismatches between the actual and presumed array responses to the desired signal. Similar types of degradation can take place when the signal array response is known precisely but the training sample size is small. The novel approach to robust adaptive beamforming is proposed in the presence of the signal steering vector mismatches. The robust RLS adaptive beamforming algorithm provides excellent robustness against the signal steering vector mismatches and small training sample size, offers faster convergence rate, makes the mean output array SINR consistently close to the optimal one and improves the unitary mismatch. Computer simulations demonstrate a visible performance gain of the proposed robust RLS algorithm.