Abstract: According to the community structure in complex social networks, we propose an evolutionary game model on community network generated by the double-degree preference mechanism under social dilemma, based on traditional Prisoner's Dilemma Game and accumulated payoff update rule. Then, we systematically analyze the effect of external connectivity density in static community networks, co-evolution time scale of strategy and structure in dynamic community network, and the noise in updating process on the emergence of cooperation and the corresponding mechanism. The results of simulation indicate that:the density of connections between communities has a negative impact on the emergence of cooperation. Although the level of cooperation in static community networks is higher than dynamic community networks, there are significant differences between static and dynamic community networks for the strategy composition, strategy stability and dynamics of cooperative evolution. In dynamic community networks, the effect of co-evolution time scale of strategy and structure on cooperation emergence shows reciprocal trend of change between pros and cons, which represents that it has a smaller cooperation level with smaller time scale under low value of temptation while it is more beneficial for cooperation with smaller time scale under high value of temptation. The effect of noise in strategy updating process on the cooperation emergence in static and dynamic community networks is monotonous, and it can significantly increases the cooperation level by introducing moderate noise.