A novel approach to suppress the maximum sidelobe level (SLL) with specific half power beam width (HPBW) of concentric circular antenna array (CCAA) is proposed. The approach is based on the cuckoo search (CS) algorithm, which is an effective optimization method for continuous problems. However, the sparse array synthesis is a discrete problem, so an improved discrete cuckoo search algorithm (IDCSA) is presented by introducing the nest location coding discretization, mapping method based on jumping path, and improved egg elimination mechanism, thereby optimizing the beam pattern of the CCAA. Simulation results show that IDCSA can obtain a lower maximum SLL with the same HPBW compared with other algorithms. Moreover, IDCSA has a faster convergence rate. In addition, the thinning rate of the antenna array can reach more than 50%, thereby resulting in cost savings after optimization.