In this paper, a new method employing Raman spectroscopy to determine thermal conductivity (TC) and thermal contact resistance (TCR) of an individual fiber was developed. Laser absorption is accounted for, but there is no need to be determined in this method. The local temperatures along the fiber longitudinal direction were determined by Raman shift. Two independent equations related to TC and TCR were established through measuring the temperature variation induced by changing electrical heating power at the center of the sample and the local temperature rise induced by a focused laser heating from Raman spectroscopy at two different positions on the sample, respectively. By solving the two equations, TC and TCR can then be obtained. This method has been validated by measuring two suspended carbon fibers.