Most evolutionary optimization algorithms have already been used for antenna design and shown promising results on improving the performance of the antenna. However, for many real-world antenna optimization problems, they are difficult to solve in that there are highly constrained and multimodal difficulty. These difficulties impede the development of antenna design. In this paper, an elliptical slot microstrip patch antenna design with these difficulties is modeled as a constrained optimization problem (COP). To address the problem, a Dynamic Constrained Multiobjective Optimization Evolutionary Algorithm(DCMOEA) is used. The experimental results show that the optimum antenna with satisfying the design requirement is obtained, and as well as we find the radiation patch should be a whole ellipse instead of subtracting with two ellipses.