With access to information is becoming more and more convenient and quick， the strategic behavior of customers is becoming more common in everyday life. In this paper， we study the optimal pricing of perishable goods in the presence of strategic customers. Monopolist sells a finite quantify of products in a certain period of time. Customers select the optimal time to buy based on the principle of utility maximization. This paper is divided into two scenarios including not replenish inventory and replenish inventory. Studies have shown that the game equilibrium exists between sellers and consumers. After a seller announces the pricing strategy， the structure of customers is divided by an optimal threshold function. The strategic behavior of customers has a significant impact on the profits of a seller. A seller can accord to the market demand and the time sensitivity of customers through proper inventory and price setting to reduce losses from the strategic behavior of customers. The situation with replenishing inventory is better than the situation without replenishing inventory only when market demand is larger.