The minimum variance distortionless response (MVDR) beamformer is known to be sensitive to steering vector error, especially when the desired signal is present in the training snapshots. The robust capon beamformer (RCB) can deal with this problem, but is computational expensive. A modification of RCB is presented utilizing the low-rank property of the steering matrix which consists of the steering vectors in the mainlobe. The computational complexity of steering vector estimation is reduced from O(N3) to O(M3). Then the norm of the weight vector is constrained and the closed-form solutions of the steering vector and the weight vector are derived. The proposed norm-constrained robust adaptive beamforming method based on low-rank property of steering matrix (NCLR-RAB) can obtain a lower computational complexity and a higher output signal-to-interference-plus-noise ratio (SINR) than RCB.