The light-weight, high-strength poly-ether-ether-ketone (PEEK) and its composite materials are the ideal candidate for a plethora of engineering applications. However, the inherent high viscosity and melting temperature of PEEK pose great challenges for the extrusion-based 3D printing process, leaving a wide knowledge gap on the properties and functionalities of novel PEEK-based composites. In this work, the PEEK/CNT composite filaments with different CNT content ranging from 1 to 7 wt% are prepared by single-screw extruder and subsequently printed with a custom-made high temperature 3D printer. The effects of CNT content and annealing on the mechanical strength and electrical conductivity of the 3D printed parts are investigated in detail. The tensile test result shows that the presence of CNT significantly enhances the mechanical strength of the composite. With 7 wt% CNT content, the maximum tensile strength and elastic modulus reaches 107.7 MPa and 1908.0 MPa, respectively, which amounts to a rise of 27.4% and 17.0% compared with the neat PEEK sample. The annealing treatment is similarly effective in strengthening the printed composites. The addition of CNT is also found to greatly improve the electrical conductivity to the PEEK, reaching 101 S/m for 7 wt% CNT. With such superior electrical conductivity, the printed PEEK/CNT composite sample exhibits outstanding electromagnetic interference (EMI) shielding performance, reaching 32.4 dB. However, additional annealing treatment decreases the electrical conductivity as wells as EMI shielding performance. Such decrease is mainly attributed to the growth of the crystals during annealing, which expels the CNTs to the grain boundaries and leads to remarkable agglomeration, which disconnects the pervasive conductive networks. The finding in this work can provide insights on the new designs of PEEK composite feedstock materials and cultivate new 3D printing strategies targeted specifically for highly-functional, high-strength novel composites.