Abstract: In this paper, a robust low sidelobe adaptive beamforming method based on second-order cone programming is proposed in view of the disadvantages of high sidelobe level of arc array conventional beamforming and high false alarm rate in the case of strong interference. This method can strictly control the sidelobe levels by the optimization design of beam sidelobes, and further improves the robustness of the low sidelobe beamformer by the covariance matrix reconstruction method. Finally, the beamformer optimization problem is transformed into a second-order cone programming problem and then solved. The results of computer simulation show that, compared with other algorithms, the proposed algorithm can achieve higher signal to interference plus noise ratio (SINR) and higher robustness in the case of various mismatches while strictly controlling the beam sidelobe levels. The pool experiment further proves the validity of the proposed method, and this method can be used in the field of sonar imaging.