Abstract: A sparse array design method for Laguerre polynomial beamformers is proposed, offering enhanced degrees of freedom in polynomial beamformer design through the introduction of Laguerre poles. To address the high-dimensional optimization challenges associated with sparse array design for Laguerre polynomial beamformers, an efficient optimization method based on the alternating direction method of multipliers (ADMM) is developed. This approach separates the array sparsification measure from the array response constraints by introducing auxiliary variables. Consequently, the original sparse array design problem is reformulated into a group-sparse regularization optimization problem, and update formulas for both the primal and auxiliary variables are derived. Simulation results demonstrate that the proposed method achieves a higher sparsification rate for array elements compared to existing designs. Furthermore, under the same array configuration, the proposed approach significantly outperforms existing methods in terms of beamforming performance.