The invention relates to a method of growing carbon nanotubes (5) on a substrate (1) using a hot-wire-assisted chemical vapor deposition method. The inventive method consists in first depositing a bilayer of titanium (12) and cobalt (13) on the substrate such that: the thickness of the titanium layer is between 0.5 and 5 nm, the thickness of the cobalt layer is between 0.25 and 10 nm, and the thickness of the cobalt layer is between half and double that of the titanium layer.