Micrometer-sized carbon tubes can be conveniently prepared via a new chemical approach by pyrolyzing the composite fibers consisting of a polypyrrole skin layer and a PET core fiber at 1000 degreesC under a N-2 atmosphere. The resultant carbon tubes were found to be amorphous carbon. After further annealing at 1000-2400 degreesC, the carbon tube structure was found, on the basis of XRD, Raman, and TEM studies, to change gradually from a disordered amorphous phase to a highly ordered graphitic phase with preferred orientation. As the annealing temperature increased from 1000 to 2400 degreesC, the graphitic crystallites of carbon tubes not only increased their sizes considerably but also tilted their stacking planes gradually toward the tube axis. Both SEM and SAD results implied that the 2400 C annealed sample may have a cylindrical layer-stacking structure similar to those of carbon nanotubes. Accompanying these enhancements of structural ordering and orientational preference of the graphitic planes, the conductivity along the tube axis of the corresponding carbon tubes was also found to increase significantly.