Coaxial multi-walled carbon nanotubes have a multi-layered structure in which a core multi-walled carbon nanotube is grown inside a sheath multi-walled nanotube from a metal-catalyst nanoparticle. In this paper, we report the optimum conditions to grow coaxial multi-walled carbon nanotubes by chemical vapor deposition. The coaxial nanotubes are studied by means of transmission electron microscopy to reveal their crystallinity and morphology. Our results show that chemical vapor deposition growth at around 1000°C with a 0.04-0.07 mg/cm3 dose of palmitic acid yields the best result.