Graphene/silicon nitride (GR/Si3N4) ceramic composites with uniformly dispersed GR sheets were prepared using spark plasma sintering. The effects of GR content on the microstructure and electrical properties of the composites were investigated in detail. With the GR content rising, the conductive GR network was formed in the composites, leading to the appearance of a percolation phenomenon, and the conductive mechanism also changed from hopping conductivity to metal-like conductivity. When the GR content reached the percolation threshold, the composites showed a negative permittivity behavior, which resulted from the low frequency plasmonic state generated by the formative conducting GR networks. The increasing GR content resulted in a higher plasma frequency and larger magnitude of negative permittivity, which was consistent with the analysis of Drude model. A relatively high dielectric loss was observed in the composites and mainly induced by the high leakage current among GR sheets. Our work is beneficial to expound the regulation mechanism of negative permittivity, and the obtained ceramic composites present some potential applications in microwave absorption, shielding and capacitors.