Abstract: A robust beamforming algorithm with uncertain weights(RBAWUW) is proposed.Unlike the constraints on the uncertainty of the array steering vector used in other documents,the proposed method is derived by adding a spherical or ellipsoidal set constraint on the uncertain weights.With this novel uncertainty constraint,the presented RBAWUW achieves a higher output signal-to-noise-plus-interference ratio(SINR) compared with the conventional robust Capon beamformer(RCB).Furthermore,the new algorithm can be efficiently computed at a comparable cost with the standard Capon beamformer.Both theoretical analysis and simulation results show that the RBAWUW method is effective and applicable.