Logistics service supply chain (LSSC) is a new type of service supply chain. This paper investigates the channel coordination issue in a two-echelon LSSC composed of one logistics service integrator (LSI) and one functional logistics service provider (FLSP) under fairness concerns. The models for a reservation price-only contract under disadvantageous inequality and advantageous inequality are established, respectively, in which the procurement cost, the potential shortage cost, and the operation cost are considered under stochastic market demand. Based on this model, the LSI's optimal reservation quantity can be determined. Furthermore, we analyze the impact of fairness concerns and the related costs on channel performance and channel coordination. The results are presented in four aspects: (1) channel coordination of the LSSC can be achieved under certain conditions when the LSI experiences advantageous inequality; (2) the spiteful behavior of the LSI leads to the reduction of the channel profit, and channel coordination cannot be achieved when the LSI suffers from disadvantageous inequality; (3) the LSI's reservation quantity and the channel profit are affected by the LSI's fairness concerns; (4) motivated by the concerns of fairness, the LSI's reservation quantity is related not only to his procurement cost and shortage cost but also to the FLSP's operation cost.