Considering the third party logistics supplier's fair concern, and assuming the product price is exogenous and endogenous respectively, this paper addresses the contract design in an online-retailer supply chain consisting of one online-retailer and one third party logistics supplier. Results show that the fair concern improves the third party logistics supplier's logistics service effort and product expected demand in exogenous price scenario, but reduces the logistics service effort and product expected demand in endogenous price scenario, and the fair concern reduces the online-retailer's expected profit and channel performance in both scenarios.