A container drayage transportation problem with the objective of low carbons is explored. This problem considers both the implicitly required repositioning of transportation resources and the transportation tasks with double time window constraints. Then, this problem is formulated as a mixed integer nonlinear programming model with two time window constraints based on an extended determined-activities-on-vertex(DAOV) graph. A time window discretization based method is designed, and the model is transferred to a pure integer linear programming model. Results of experiments show that the precision and speed of this solution method is acceptable. The comparison with the problems in which speeds are given validates the effectiveness of the proposed model.