Abstract: Connectivity patterns in delay tolerant networks can be modeled as Edge-Markovian graph and this model is better than traditional negative exponential model. In this paper, the optimal control problem of two-hop routing algorithm is explored with energy constraint under the Edge-Markovian graph. Considering that the source forwards the message with certain probability and the probabilistic two-hop routing method is used to decrease the energy consumption, the problem turns into the finding of the optimal probability to maximize the delivery ratio with energy constraint. Thus, a theoretical model for the problem is proposed based on the discrete time Markov process. We further prove that the optimal forwarding probability conforms to the threshold form. Simulation and numerical results show the correctness of the theoretical model.