Due to the limited resources, nodes in Delay Tolerant Network (DTN) behave selfishly, i.e. nodes refuse to help forward message for others. In order to improve the cooperative behavior of nodes, and enhance the overall network performance, a new incentive mechanism of node behavior based on Evolutionary Game Theory (EGT) was proposed. In the proposed mechanism, the prisoner's dilemma model was employed to establish payoff matrix between the node and its neighbors. Then, based on the degree centricity, social authority of the node was defined. Further, when designing the strategy update rule, the influence of social authority was considered. That is, nodes with higher social authority were selected from the current neighborhood to imitate and learn. Finally, on the basis of real dynamic network topology, the simulation experiments were conducted by the Opportunistic Network Environment (ONE) simulator. The simulation results show that, compared with the Fermi update rule which chooses neighbors randomly, the strategy update rule which considers the social authority can promote the cooperative behavior, accordingly, improve the overall performance of the network.