Concentric circular antenna arrays (CCAAs) can obtain better performance than other antenna arrays. However, high overhead and excessive sidelobes still make its application difficult. In this paper, we consider the sparse synthesis optimization of CCAAs. Specifically, we aim to turn off a specific number of antennas while reducing the sidelobe of CCAAs. First, we formulate an optimization problem and present the solution space. Then, we propose a novel evolutionary method for solving the optimization problem. Our proposed method introduces hybrid solution initialization, hybrid crossover method, and hybrid update methods. Simulation results show the effectiveness of the proposed algorithm and the proposed improvement factors.