As the quality of new products is ex-ante uncertain, social influence plays an important role in the diffusion of a new product. An important question is how to expand public knowledge about consumer experience with a new product by using promotion strategies. This paper discusses the impact of advance selling strategies on a three-echelon supply chain when upstream enterprises launch a new product facing strategic consumers under social influence. This problem is modeled as a Stackelberg game, and a two-advance-selling-discount model is presented. Furthermore, we consider the impact of advance purchase behavior on the financing strategy when the retailer places an advance order. Several results are obtained: (i) the consumers’ utility in the second period is increasing in the number of predecessors. (ii) Upstream enterprises will provide deeper advance selling discounts when consumers become more patient or predecessors have a greater influence on imitators. Moreover, the total demand will increase when the consumer’s discount factor decreases or the impact intensity of predecessors increases. However, high innovation levels will drive enterprises to set high advance selling discounts. We also obtain the condition under which the total demand increases quickly as the innovation level changes. (iii) The two-advance-selling-discount model yields Pareto-improved results compared with the case where there is no advance purchase, though it cannot coordinate the supply chain. Finally, we extend the model to analyze the two-advance-selling-discount model with a minimum order quantity constraining the precommitted order quantity, and we show this can allow the enterprises to increase their profits. We also determine a condition under which the upstream enterprises should put a constraint on the minimum order quantity.