Suppliers’ offering delay payment terms to retailers can be regarded as a type of price reduction. In today’s ever competitive marketplace, offering delay payments has become a commonly adopted method to suppliers. Most of the inventory models with permissible delay in payments assumed that the entire lot size is delivered at the same time. However, in practice, goods ordered are usually arrived overtime in separate batches. In this study, we discuss an inventory problem with a finite replenishment rate under trade credit for two payment methods. We establish a theorem to find the optimal solution for each payment method. Numerical examples are also given to illustrate the solution procedure. Finally, to investigate the effect of changes of some main parameter values on the optimal solution, a sensitivity analysis is performed and some management interpretations are proposed.