According to the problem of channel coordination in supply chain, a Stackelberg game coordination mechanism is presented, in which the seller is the leader initializing the minimum replenishment periods and quantity discount policies, and each buyer is the follower responding with the optimal stock policy. The cost optimization model of the seller under each buyer's deterministic demand is established, in which two different quantity discounts are compared. Through the application of genetic algorithm, simulation works are carried out to compute the Stackelberg equilibrium off-line for the problem in Liaoyang petroleum fabric company.