Abstract: Aiming at the problem of beam width optimization synthesis in antenna array at given sidelobe level, a pattern synthesis method of antenna array based on iterative adaptive convex optimization is proposed, and the process of the algorithm is given. Under the condition that the sidelobe level is given, the beam pattern of the antenna array is optimized by the convex optimization algorithm, and the bi-partitioning strategy is used to search the beam width iteratively, the optimization synthesis of the beam width under the control sidelobe level is realized. Firstly, constraints are added to the main lobe of the pattern to ensure that the maximum radiation direction is directed towards the target direction. Secondly, the main lobe zero power beam width corresponding to Chebyshev excitation distribution pattern is used as the reference point of the initial beam width. Finally, when the initial sidelobe level is too low, resulting in the distortion of the main lobe of the pattern, the pattern under the lowest sidelobe level that can be realized by the algorithm is optimized. The simulation results show that the proposed algorithm can obtain the narrowest pencil beam pattern of the array antenna at a reasonable sidelobe level. On the basis of the ideal point source array results, the actual antenna is introduced to obtain the full wave simulation results, and the feasibility of the method is verified.