Highly thermally conductive carbon nanotube/polybenzimidazole polymer nanofiber composites were produced by core-shell electrospinning. The in-plane thermal conductivity increased by factor of 50 for 1.94 wt.%. carbon nanotubes in the composite nanofibers. The high thermal conductivity results from the excellent nanotube alignment in the core of the polymer fiber and the use of liquid crystal polybenzimidazole as a matrix and shell polymer. (C) 2012 Elsevier Ltd. All rights reserved.