In this paper, a local enrichment strategy was adopted to prepare carbon nanotube (CNT) enriched polylactic acid (PLA) composite filaments, which were used to fabricate the corresponding conductive 3D-printed parts by fused deposition modeling (FDM) technology. Combined with computer simulation, the carbon nanotubes (CNTs) were found to be successfully kept and supported on the surface of filaments after 3D-printing. With this strategy, the prepared 3D-printed parts showed a remarkably enhanced electrical conductivity, which was approximately eight orders of magnitude higher than that of the conventional 3D-printed parts at the same loading of CNTs. This encouraging result provided a new method for fabricating the high-performance parts through FDM printing, and also opened up new routes for 3D-printing technologies to prepare other advanced binary or multicomponent polymer composites.