In this paper, we apply game theory to study the price competition between drugstores and hospitals in China’s pharmaceutical supply chain. Motivated by drug shortages and price disparity problems, we build a simplified model with one supplier, one hospital, and one drugstore in which the sellers sell one kind of drug and compete on price. The hospital receives a discount from the government when ordering the drug and both sellers face a price-sensitive and uncertain demand. The existence and uniqueness of a Nash equilibrium are proved and closed-form solutions are found for linear demand cases. We characterize the pricing and ordering decisions of the hospital and drugstore. The analysis shows that high ex-factory price, high price sensitivity, and a small discount are three factors contributing to drug shortages. We consider two special kinds of linear demand to obtain insights into the drug price disparity problem.