The paper proposes the novel numerical approach, called phasor particle swarm optimization (PPSO), for the optimal design of structures under natural frequency constraints. The proposed scheme develops the phasor theory in mathematics directly within the PSO algorithm. In essence, a phase angle incorporating the periodic sine and cosine functions is applied during the optimization process to model particle control parameters. This technique enables the fast-learning strategy of the particle velocity and is thus able to capture the optimal sizing distributions of structural members under some specified conditions at modest computing efforts. The application of the proposed method is illustrated for the optimal design of dome structures subjected to the responded natural frequency limits. A number of numerical examples (including benchmarks and realistic structures) successfully tested show the robustness of the PPSO scheme and the accuracy of computed design solutions through comparisons with those reported by some meta-heuristic algorithms.