We are concerned with a multiple replenishment contract with a purchase price discount in a supply chain. The chain is composed of one supplier, one buyer and consumers for a product. The replenishment contract is based upon the well-known (s, Q) policy but allows contracting several firmed orders at a time with a price discount. Due to a larger forecast error of the future demand, the buyer should keep a higher level of safety stock to provide the same level of service of the usual (s, Q) policy but can reduce his purchase cost by placing larger quantity. Thus there exists a trade-off between the price discount and inventory holding cost. We present a model for the contract and an algorithm to find the optimum number of the firmed orders. Computer experiments show that the algorithm finds the global optimum solution very fast.