Beam capture efficiency (BCE) is one key factor of the overall efficiency for a microwave power transmission (MPT) system, while sparsification of a large-scale transmitting array has a practical significance. If all elements of the transmitting array are excited uniformly, the fabrication, maintenance, and feed network design would be greatly simplified. This paper describes the synthesis method of the sparse uniform-amplitude transmitting array with concentric ring layout using particle swarm optimization (PSO) algorithm while keeping a higher BCE. Based on this method, uniform exciting strategy, reduced number of elements, and a higher BCE are achieved simultaneously for optimal MPT. The numerical results of the sparse uniform-amplitude concentric ring arrays (SUACRAs) optimized by the proposed method are compared with those of the random-located uniform-amplitude array (RLUAA) and the stepped-amplitude array (SAA), both being reported in the literatures for the maximum BCE. Compared to the RLUAA, the SUACRA saves 32% elements with a 1.1% higher BCE. While compared to the SAA, the SUACRA saves 29.1% elements with a bit higher BCE. The proposed SUACRAs have higher BCEs, simple array arrangement and feed network, and could be used as the transmitting array for a large-scale MPT system.