This paper aims at understanding coevolutionary dynamics of cooperative behaviors and network structures of interactions. We constructed an evolutionary model in which each individual not only has a strategy for prisoner's dilemma to play with its neighboring members on the network, but also has a strategy for changing its neighboring structure of the network. By conducting evolutionary experiments with various settings of the payoff matrix, we found that the coevolutionary cycles of cooperative behaviors of individuals and their network structures repeatedly occurred when both the temptation to defect and the cost for playing a game were moderate.