Electrochemical deposition of copper on a carbon nanotube (CNT) fiber from a copper sulfate - sulfuric acid bath was studied in order to produce a carbon nanotube-copper composite wire. The high resistivity of the aerogel-spun fiber causes a non-uniform current distribution during deposition, which results in a drastic drop in the copper nuclei population density as sufficient overpotential is not available beyond a certain distance from the current feed point. Copper was found to fill the pores between CNT bundles from Focused Ion Beam (FIB) cut cross-sections confirming that aqueous based electrolytes can fill micropores between as-spun CNTs in a fiber network. The speed at which copper grows on the fiber surface was identified at ca. 0.08 mm/s with 1 mA applied current. The copper cladding showed columnar growth with a grain size an order of magnitude higher than the CNT-Cu region. The resulting composite was found to have specific conductivity similar to that of pure copper i.e. 98% of copper with 0.2 w-% of CNT, exhibiting a ninefold increase from the pure CNT fiber. Self-annealing was shown to decrease the resistance of the composite.