Two types of graphene nanoplatelets (xGn and N02) were added to ppoly(lactic acid) (PLA) through solvent mixing to prepare PLA nanocomposites with the aim of producing electrically and thermally conductive PLA products suitable for advanced applications. Transmission electron microscopy (TEM) and X-ray diffraction (XRD) showed that N02 was fully exfoliated and homogenously dispersed in the PLA matrix, while xGn was poorly dispersed with stacked multi-layer structures. Rheological tests were used to characterize the viscoelastic behavior of the nanocomposites and several models/scaling relations based on the rheological results were employed to determine the structure and properties of the percolated graphene networks. The electrical conductivity of the nanocomposites increased by more than twelve orders of magnitude after the graphene concentration reached the percolation threshold. The threshold values obtained from different models showed reasonable agreement.