All-solid-state batteries are considered as one of the attractive alternatives to conventional lithium-ion batteries, due to their intrinsic safe properties benefiting from the use of non-flammable solid electrolytes in ASSBs. However, one of the issues in employing the solid-state electrolyte is the sluggish ion transport kinetics arising from the chemical and physical instability of the interfaces among solid components including electrode material, electrolyte and additive agents. In this work, we investigate the stability of the interface between carbon conductive agents and Li10GeP2S12 in a composite cathode and its effect on the electrochemical performance of ASSBs. It is found that the inclusion of various carbon conductive agents in composite cathode leads to inferior kinetic performance of the cathode despite expectedly enhanced electrical conductivity of the composite. We observe that the poor kinetic performance is attributed to a large interfacial impedance which is gradually developed upon the inclusions of the various carbon conductive agents regardless of their physical differences. The analysis through X-ray Photoelectron Spectroscopy suggests that the carbon additives in the composite cathode stimulate the electrochemical decomposition of LGPS electrolyte degrading its surface during cycling, indicating the large interfacial resistance stems from the undesirable decomposition of the electrolyte at the interface.