Length dependence of the thermal conductivity of （5, 5） carbon nanotube at 300 K and 1000 K is studied by nonequilibrium molecular dynamics simulations. At room temperature the thermal conductivity shows linear length dependence for the tube length less than 40 nm, which shows completely ballistic transport. The calculated ballistic thermal conductance per unit area is 5.88×109 Wm-2K-1. The thermal conductivity increases with the increase of the nanotube length, but the increase rate decreases as the length increases. It shows that the phonon transport is in the ballistic-diffusive regime, and transits from ballistic to diffusive with increase of the tube length. The thermal conduction is close to completely diffusive transport and the ballistic transport can be ignored when the nanotube is longer than 10 μm. In the simulations, the power exponent of the thermal conductivity of carbon nanotube to the tube length decreases by decaying exponential function as the tube length increases. Different from one-dimensional material, in the thermodynamic limit, a completely diffusive transport will dominate the thermal transport in carbon nanotubes, and the thermal conductivity will converge to a finite value.