In 1995, Padmanabhan and Vrat presented inventory models for deteriorating items with a constant selling price and stock dependent selling rate . Based on the result, in 2000, Kun-Jen Chung, Peter Chu and Shaw-Ping Lan devoloped the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions of the profit per unit time functions without backlogging and with complete backlogging. Actually, the selling price need not be constant, it may be variable . This paper puts forward an EOQ model when the selling price is variable without backlogging, discusses the existence and uniqueness of optimum solution. The example is provided to illustrate the model. The theoretical evidence is provided for the inventory system to make management decision.