In this work, the analysis of interfacial consistency on phase-field modeling of solid-state sintering is performed. A phase-field model is termed interfacially consistent if no artificial void is produced at junctions of grain boundaries in fully dense powder compacts under sintering. A mathematical analysis of the well-known and widely employed phase-field model, termed Model I in this work, found that Model I may offer a spurious driving force for producing artificial voids at the junctions of grain boundaries, and that the ratio of specific grain boundary energy to specific surface energy and the number of grain boundaries meeting at junctions significantly affect the locally generated non-physical porosity. Inspired by Model I, a novel phase-field model, termed Model II, is proposed to protect interfacial consistency by decoupling the respective surface energy and grain boundary energy contributions to the total free energy of the system. The theoretical analysis of both Model I and Model II is also numerically confirmed. Finally, Model II is validated by comparing the phase-field dihedral angles and dynamic neck growth with the ones from analytical models and experiments.