The evolution of cooperation among unrelated individuals in human and animal societies remains a challenging issue across disciplines. It is an important subject also in the evolutionary game theory to understand how cooperation arises... The subject has been extensively studied especially in Prisoners' dilemma game(PD) but the emergence of cooperation is also an important subject in public goods game(PGG). In this article, we consider coevolutionary PGG on complex networks where both the topology of the networks and strategies that players adopt under the influence of game dynamics varies. Though cooperators can contribute a fixed amount per game in PGG on networks in the previous studies, the cooperators contribute a fixed amount per member of the group in PGG of this article. The latter is seemed to be more natural than the former model. These models lead to great differences in both PGGs. We study what effects on the evolution of player's strategies, defection and cooperation and the average payoff does the interaction between the game dynamics and the network topology bring. Moreover by comparing the models that do not depend on game dynamics to the models without topology changing, we intend to uncover the effect of the topology chnage and the game dynamics on the promotion of the cooperation. As result we intend to clear in what situations cooperation strategy is promoted or preserved by investigating them by making computer simulations. We also investigate the relation between the ratio of the cooperator and the average payoff over all players. Furthermore we study how do the topology of initial networks have an influence on the cooperation and the average payoff. (read more)