It has been generally observed that the credit period has become a major concern for most of retailers, as it not only has direct influence on inventory and finance, but also on the demand of an item. Unfortunately, for deteriorating items, the impact of the credit period on demand has not received much attention in the literature, whereas in reality, the length of the credit period offered by the supplier/retailer has a positive impact on the demand rate. Furthermore, it is generally observed that at the initial stage the credit period may not be effective in realising the demand but as the credit period increases it has a significant impact on demand and gradually reaches its saturation level. In order to incorporate this phenomenon in a supply chain of a single supplier single retailer and multiple consumers, a credit-linked demand function has been considered to determine the optimal replenishment time as well as the credit period for a retailer. Using the theorem, the optimal replenishment policy for deteriorating items has been derived for the retailer. Finally, results have been validated with numerical examples followed by a sensitivity analysis.