One of the main roles of the nuclear fuel bundle spacer grid (SG) is to safely support the fuel rods (FRs) through springs and dimples. The SG design is an important matter for nuclear power plant operation when a damaged FR could release fission products. For this work, Particle Swarm Optimization (PSO) is applied to define the geometries of the springs and dimples existing in a SG. Other algorithms had been used to optimize these geometries but not PSO. This paper proposes a PSO variable model and its fitness function in order to define an optimized geometry for the spring and the dimple so that they can provide sufficient gripping forces and minimize stresses. The implemented PSO was able to generate geometries of springs and dimples with stresses minimized and with a specific required stiffness value. The results of these two characteristics are compared with other results in the literature. For further work, PSO will be used to optimize other important design characteristics of a SG: grid-to-rod fretting, coolant flow-induced vibration, and the function of mixing coolant.