The thermal contact resistance is a difficult problem that has puzzled many researchers in measuring the intrinsic thermal conductivity of an individual carbon nanotube (CNT). To avoid this problem, a non-contact Raman spectra shift method is introduced, by which we have successfully measured the thermal conductivity (kappa) of an individual single-walled carbon nanotube and a multi-walled carbon nanotube. The measured kappa values are 2400 W m(-1) K(-1) and 1400 W m(-1) K(-1), respectively. The CNT was suspended over a trench and heated by electricity. The temperature difference between the middle and the two ends of the CNT indicated its intrinsic heat transfer capability. The temperature difference was determined by the temperature-induced shifts of its G band Raman spectra. This new method can eliminate the impact of the thermal contact resistance which was a Gordian knot in many previous measurements.