Grounding systems are necessary for safety of people to be exposed to dangerous voltages during any fault and for equipment by keeping their proper operation. In design of grounding grids, it is important to minimize the cost of grounding grid by considering tolerable touch voltage and step voltage values defined in regulations. For this purpose it is necessary use an optimization tool in order to have an effective design. In this paper, a method for designing grounding grids by using a genetic algorithm is presented. The aim is to minimize the cost function of the grounding grid, while the design parameters are kept according to limits defined by IEEE-Std-80. For the design of the grounding system, which comprises of 100 m x 100 m square grounding grid and ensures tolerable touch and step voltages at reasonable costs, Genetic Algorithm (GA) has been utilized. This design has been made with uniform soil model, and grid parameters which are effective at touch and step voltages have been determined via GA method. Furthermore, burying depths and rod lengths have been compared in order to keep the costs at minimum level. During the studies Matlab has been used for the genetic algorithm application. Different parameters have been studied in order to see the effectiveness of the proposed method and designed grid has been compared with real grounding grids, validating the proposed solution.