In this study, Grey Wolf Optimization (GWO), which is a new method with swarm intelligence is compared with another metaheuristic optimization method, Particle Swarm Optimization (PSO), using optimization benchmark functions. Simulation studies on test functions are presented as a table by obtaining mean, standard deviation, best and worst values. In addition, the effects of population and iteration number change on the GWO algorithm are presented in separate tables. The GWO algorithm has establish a good balance between exploration and exploitation. Simulation studies have shown that GWO has better convergence performance and optimization accuracy.