Summary: In order to solve the “dimension curse”, the paper proposes a new discrete approximate iteration method to solve the continuing convex dynamic programming model. Firstly, according to the network approach, the state variables are discretized and the model is transformed into a multiperiod weighted digraph. Secondly, the max-plus algebra is used to solve the shortest path that is the admissible solution. Thirdly, based on the admissible solution, the iteration is continued until the two admissible solutions are close to each other. The method is proved to be convergent and linearly convergent. Finally, an example shows that the method is highly effective.