Considering the un-deterministic transportation networks, the paper proposes the change of the route choice decisions under the stochastic transportation networks. The route choice behavior is described as a choice for a time shortest route which is subject to a time-reliability level. The paper also considered this new route choice behavior in the stochastic user equilibrium model, and proposed stochastic user equilibrium model based on the optimized reliability travel time route choice behavior in the stochastic networks. The equivalence and uniqueness of the solution of the model are demonstrated. Numerical results of a small network show that the proposed model can reflect the real traveler’s route choice behavior in stochastic transportation networks.