In this thesis we investigate the effect of topology of small-world networks on population evolution. The population evolves according to the Fermi imitation rule in two ways by considering two strategies; cooperation as the resident and defection as the mutant, and defining a payoff matrix. The evolution process was simulated with Python programming language. In the first method, the selected node imitates the neighbor with highest score with the Fermi probability and we observe that for all values of the rewiring probability and the size of network and small average degrees, two strategies eventually coexist. But, as the average degree increases, the fixation probability increases. In this method the rewiring probability and the size of network has no effect on the population evolution. In the second method, the selected node imitates a random neighbor with the Fermi probability and we observe that as the rewiring probability or the average degree increases, the fixation probability and the fixation time of defection decrease. However, by increasing the size of network, the fixation probability also increases. In this method no coexistence is observed and all realizations necessarily lead to fixation or extinction of defection.