This paper studies a pull supply chain where a capital-abundant retailer sources from a capital-constrained manufacturer and offers the manufacturer a special buyer financing with a minimum purchase quantity commitment. We characterize the equilibrium solutions for different financing schemes, including bank financing and the special buyer financing. Compared with bank financing, we find that the special buyer financing always benefits the whole supply chain. When the margin of the business is high, the retailer (manufacturer) will be better off (worse off) under special buyer financing. When the margin of the business is moderate, both the retailer and the manufacturer can benefit from the special buyer financing. When the margin of the business is low, the retailer refuses to offer a loan. In addition, we study the impact of demand variability on the performance of the supply chain and find that the special buyer financing can resist the risk caused by demand variability. Further, we extend the model and find that the retailer and the manufacturer have different attitudes towards differential wholesale prices under the special buyer financing. Finally, we examine the value of quantity commitment in buyer financing, and our results show that whether the quantity commitment can play a positive role in buyer financing scheme depends on the margin of the business.