This paper presents a continuous review inventory model with a lost sales assumption. The model is unique due to the inclusion of a time discount. Whenever the supplier faces the likelihood of being out of stock, he may issue a discount to motivate customers to accept delayed deliveries and thus avoid the occurrence of lost sales. We propose a control policy with four parametersR1,Q,R2andTwhereR1andQare the normal reorder point and quantity, respectively andR2andTare the triggers for this time discount. During each replenishment cycle, if the on-hand inventory drops toR2 at or before T after the reorder time epoch, the time discount will be granted. A derivation as well as a solution approach for the total cost function are provided. Based on computational results, such a system with a time discount is superior to that without a time discount in terms of minimizing the total system cost. Finally, we compare the performance of the time discount and the emergency ordering approaches.