In the logistics service supply chain (LSSC), quality supervision and coordination is an important approach that can ensure the effective operation of LSSC and obtain more customers. This paper aims to study the quality decisions of the functional logistics service provider (FLSP) and the logistics service integrator (LSI) when a service quality defect guarantee is promised by the FLSP. Assuming that customer demand is a function of the quality defect guarantee of the FLSP, the optimal quality decisions of the LSI and FLSP are presented under three typical game modes: Nash game, Stackelberg game, and centralised decision. Numerical analysis is conducted to show how the quality parameters of the customer affect the optimal quality decision-making behaviour of the LSI and FLSP. The research results indicate that, under all three game modes, the optimal quality defect guarantee of the FLSP increases as the customer punishment increases, and decreases as the elasticity of the customer demand for the quality defect guarantee increases. In addition, under all three game modes, the optimal quality supervision effort of the LSI is an increasing function of both customer punishment and elasticity of the customer demand for the quality defect guarantee.