This paper analyzes permissible delay in payment of a two-level supply chain for deteriorating item considering cash constraint. We obtain the annual profit model of supply chain member and the optimal order policy of the retailer with cash constraint and without cash constraint. Furthermore, a stackelberg game model between the supplier and the retailer is put forward and a PSO is presented to achieve the optimal solution of the problem. Finally, numerical examples are developed to explore the impacts of some supplier's parameters on supply chain members. Outcomes of the paper show that the revenue of the retailer and the supplier increase as the delay period in payment increases before certain threshold point. However, after the threshold, the revenue of them may decrease as the delay period increase. In addition, retailer with cash constrain prefers delay strategy, supplier can also gain more by increasing wholesale price and interest rate.