In managing an international project, claims are very important. In this paper, a complete information dynamic game model is designed; with the Nash equilibrium values, the huge influence of claim cost on claim strategy is testified and the importance of claims to both sides of a contract especially the contractor is elucidated. Claim chances are also discussed with game theory. At last, from the angle of a repeated game and by comparison with Pareto optimization and Nash equilibrium values, it is concluded that the best payoff can be obtained with a honest attitude and through cooperation between companies.