In this paper, a new hybrid optimization approach based on Convex-Genetic-Taguchi Algorithm which is developed for the pattern synthesis of the linear antenna arrays is presented. Convex-Genetic-Taguchi Algorithm uses Convex optimization, Genetic Algorithm and Taguchi Method in order to obtain desired side lobe level and half power beamwidth. The results obtained by Convex-Genetic-Taguchi Algorithm, Convex Optimization, Genetic Algorithm, Taguchi Method and Hybrid Taguchi-Genetic Algorithm are compared. The obtained results show that Convex-Genetic-Taguchi Algorithm improves the results of Convex Optimization. By the new hybrid algorithm optimization goals are reached faster and better than the other methods compared with.