In recent years, studies on the thermal properties of single wall carbon nanotubes are of great research interest in the area of thermal management. The heat energy in solids is transferred by the quantized lattice vibrations called phonons and it is possible to estimate the lattice thermal conductivity by Raman spectroscopy. Here we estimate the thermal conductivity of nanometer thick suspended single wall carbon nanotube mat by laser Raman spectroscopy. From the temperature and laser power dependent frequency shift of the A1gmode of the G band, the thermal conductivity is estimated to be about 18.3 Wm-1K-1. The obtained result is supported by our theoretical study that suggests the thermal conductivity of the carbon nanotube mat is contributed both by the intra and inter-tube thermal transport. The calculated inter-tube thermal conductivity is about 0.7 Wm−1K−1, which is much less than the intra-tube thermal conductivity.