To suppress the beam distortion and sidelobe rise caused by array element position offset, a robust minimum mainlobe low sidelobe beamforming method based on convex optimization is proposed. The constraint of element position offset is introduced into the optimization object on the basis of the element weight vector optimization, in which the improved dichotomy and second-order cone programming method is used for high calculation efficiency. The results of Mente Carlo experiments show the synthesized beam of proposed method outperforms the conventional method in beamforming with array element position offset, its characteristics of narrow mainlobe, accurate direction and low sidelobe enable the proposed method suitable for large beamforming applications.