In waterway and port projects，especially the international contract projects, the sum of construction claim is often
huge and the duration of claim negotiation is often long and the influence of discount factor to the claim cannot be ignored. But nowadays the models of construction claim negotiation are not suitable enough. This paper establishes the model of water trans port and port projects claim negotiation based on the game theory，considering the discount factor. Then this paper concludes that the procedure of barging will be shortened if considering the discount factor. The study case verifies the application of the established model.