Abstract: In view of the problem of specifying the main lobe and side lobe levels in beam-pattern synthesis, a pattern synthesis method based on multi-approximation optimization and consistent alternating direction method of multipliers (CADMM) is proposed. The proposed method is to minimize the ratio of the maximum power of the side lobe to the minimum power of the main lobe under the limit of the power sum of the side lobe and the main lobe. Firstly, auxiliary variables are introduced to decouple the numerator and denominator and separate them into two independent sub-problems. Secondly, the two independent sub-problems are approximated as sub-problems with unified forms by using log-sum-exp approximation method, and the transformed objective functions are approximated by two approximation algorithms. Finally, the CADMM is used to eliminate the equality constraints and solve weighted vectors iteratively, obtaining the specific solution during each iteration. Morevoer, the complexity of the algorithm is also analyzed in the paper. The experimental results show that the proposed mehtod can obtain low side lobe level as well as achieve beam-pattern synthesis very well; and it is suitable for arbitrary one-dimensional linear array configuration. This study also provides an idea to solve non-convex fractional programming problems and improves the performance of beampattern synthesis algorithms.