Synthesis of desired radiation patterns without an optimization algorithm is usually time consuming and inefficient. To achieve a desired radiation pattern such as cosecant squared beam and contoured beam, different evolutionary algorithms such as genetic algorithm (GA), particle swarm optimization algorithm, and invasive weed optimization algorithm have been used to find the excitation of radiation elements. Adaptive genetic algorithm (AGA) optimizer is a robust, stochastic search method, modeled on the principles and concepts of natural selection and evolution. As an optimizer, the powerful heuristic of the AGA is effective for solving complex and related problems. An improved AGA is proposed, in allusion to the characteristics of optimizing designs of antenna arrays which have many parameters and complicated structures. This algorithm constructs an adjustble formula to produce the crossover rate and mutation rate based on a logistic curve equation. In the way of combining roulette wheel selection and elitist strategy, this algorithm searches for the optimal solution in the global space, and is compared with the classical GA; the improved AGA has a better performance in seeking the solution. Taking the mutual coupling between the elements into account, we design the X band extended cosecant squared beam micro-strip antenna arrays based on the improved AGA. Specifications of the antenna are as follows:a -3 dB beam width in height is from 0° to 12°, a -10 dB beam width in height is from 12° to 65°, and a total height coverage is 65°; a frequency band ranges from 8.5 to 9.8 GHz and its center frequency is 9.05 GHz. Simulation results show that the fitness increases from 0.07 to 0.09, and the quality of the synthesized radiation pattern has a great improvement, which verifies the superiority of the improved AGA proposed in this paper. In addition, the prospect of the designed antenna which has an extended cosecant squared beam is promising in air-surveillance radar systems, where the radiation pattern of the antenna will compensate for the free-space loss.