Based on the molecular dynamics method and improved reactive empirical bond order potential, Green-Kubo function is used to calculate the thermal conductivity of carbon nanotube. The overlapping method is used which shortens the simulation time greatly. The result shows that the most significant contribution to the thermal conductivity is presented by the auto correlation of interactive force of atoms. The thermal conductivity decreases as the tube diameter increases. The thermal conductivity increases as the temperature increases for temperature lower than 300K and converges to a constant when the temperature rises above 300K. The thermal conductivity of the single-walled carbon nanotube ranges from 1000W/mK to 4000W/mK, and the results are in good agreement with the experimental data.