Credit payment strategies have been implemented widely in the online retail industry. This work studies an online-retail supply chain involving credit period and selling price-dependent demands. The participants of the supply chain form a Stackelberg game where the supplier as a follower sells products to the customers through an online platform provider, who as a leader provides a credit period to customers and charges the supplier based on the quantity of goods sold. We study and compare the supply chains when the online platform provider adopts the cash payment and credit payment strategies, respectively, to investigate the effects of the credit period, the selling price and the default risk on supply chain system performance. We also investigate these supply chains under both the centralized and decentralized settings and provide an example to illustrate a simple allocation mechanism to coordinate the decentralized supply chain. Finally, an extension of the supply chain with credit payment is given.