In this paper, we consider a revenue-sharing and network investment problem between an Internet service provider (ISP) and a content provider (CP) by applying the dynamic agency theory. We formulate the problem as the principal-agent problem where the ISP is the principal and the CP is the agent. The principal-agent problem is transformed to a stochastic optimal control problem in which the objectives of ISP are to find an optimal revenue-sharing strategy and a network investment strategy, and to advise an incentive compatible effort level to the CP. The sufficient conditions for the existence of the optimal revenue-sharing strategy, the optimal investment strategy and the incentive compatible effort to the CP are obtained. A numerical example is solved to show the existence of such strategies. The practical implications of the results obtained in the paper will also be discussed.