This invention relates generally to a method for growing carbon fiber from single-wall carbon nanotube (SWNT) molecular arrays. The carbon fiber which comprises an aggregation of substantially parallel carbon nanotubes may be produced by growth (elongation) of a suitable seed molecular array. The first step is to open the growth end of the SWNTs in the molecular array. Next, a transition metal catalyst is added to the open-ended seed array. In the next step, the SWNT molecular array with catalyst deposited on the open tube ends is subjected to tube growth (extension) conditions. The carbon supply necessary to grow the SWNT molecular array into a continuous fiber is supplied to the SWNT molecular array tip heated to a temperature sufficient to cause growth to any desired length. The continuous carbon fiber can also be grown from more than one separately prepared molecular arrays or templates.