The low earth orbit (LEO) satellite system is a key point in the research of the next generation network, 6G. Phased array antenna is an important component of the LEO satellite antenna system, and its research and development have attracted more and more attention. LEO satellites require a reduction in the number of antenna arrays to achieve the effect of simplifying the array structure. Based on the above, this paper proposes an array sparse algorithm based on the combination of amplitude density and genetic algorithm (ADGA) to simplify antenna array arrangement. The task is transformed into an array sparse problem with the goal of minimizing the peak side lobe level (PSLL) of the beam while meeting a certain sparsity rate and ensuring that the width of the main lobe is basically unchanged. The non-iterative algorithm based on the amplitude density is used to quickly give an initial solution of array sparseness. Then, the improved genetic algorithm is used for further optimization, where the array element symmetry constraints is proposed to enhance the optimization effect. The simulation results show that, compared with the genetic algorithm and the traditional analytical algorithm, the proposed algorithm reduces the number of array elements and effectively reduces the PSLL of the beam generated by the LEO satellite under the premise of keeping the main lobe width basically unchanged.