A new iterative adaptive beamforming (ABF) algorithm based on conventional beamformers is proposed in order not only to steer the main lobe toward the desired signal and place radiation pattern nulls toward respective interference signals but also to achieve the desired sidelobe level (SLL). Thus, the algorithm becomes less susceptible to unpredicted interference signals than conventional beamformers. In each iteration, the algorithm finds the direction of the peak of the greatest sidelobe, which is considered as direction of arrival (DoA) of a hypothetical interference signal, and the conventional beamformer is then employed to find proper antenna array weights that produce an extra null toward this direction. The iterative procedure stops when the desired SLL is obtained. The algorithm is applied on three conventional beamformers and is tested for various signal DoA, while the direction deviation of the main lobe and the nulls is recorded, to evaluate the algorithm in terms of robustness. The proposed algorithm needs a few iterations to achieve the desired SLL and thus is much faster than any evolutionary iterative method employed for sidelobe suppression. Finally, unlike methods that employ neural networks (NNs), the proposed algorithm does not need any training to become functional.