This paper incorporates the fairness concerns into a logistic service supply chain(LSSC) which consists of a logistics service integrator(LSI) and a functional logistics service provider(FLSP). The logistics demand function is assumed to be influence by LSI's corporate social responsibility and FLSP's service. a cost-sharing decision model and A cost sharing-two part tariff decision model are established to investigate how fairness concerns may affect CSR level, logistic service, profits of channel members, total channel profit and coordination. Results show that the fairness concerns of the channel numbers do not change the coordination situation of LSSC under decentralized decisions and two-part tariff decisions. The two-part tariff contract can achieve a win-win situation between LSI and FLSP and better-off the LSSC's performance. More results and management insights can also be derived about fairness concerns.