Abstract: In the real world, networks often have "scale-free", "high clustering" and "interconnection" features. In order to model these characteristics, we proposes an algorithm for constructing the interdependent Holme-Kim network and use tools of complex networks and evolutionary game theory to research the emergence of cooperation in our network model, where a Prisoner's Dilemma game is played. Through simulation experiments, the effects of the connection degree, the connection probability mentioned in the algorithm and the temptation to defect in the payoff matrix of the Prisoner's Dilemma game are studied. Our results show that the lower the connection degree and the connection probability on the same scale of the network, the easier the formation of cooperative behavior on the network. When the parameter of the temptation to defect is more than a certain threshold, a great number of defectors will be on the networks.