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The control and maintenance of inventories is a problem common to all enterprises in any sector of a given economy. Two fundamental question that must be answered in controlling the inventory are when to replenish the inventory and how much to order for replenishment. The (Q,r) inventory models attempt to answer the two question under a variety of circumstances. Studies have shown, (1) that a company that ignores lead-time demand variability may suffer great financial damage, (2) that the gamma distribution provides the most common best fit to lead-time demand for variety of inventories items, (3) that a fixed lead-time demand assumption or a normal approximation to it will often yield significant errors (Namit and Chen, 1998).This research performed an efficient and accurate algorithm for solving (Q,r) inventory model with gamma lead-time demand.