We studied the adsorption and dynamical behavior of pyrene molecules on single-wall carbon nanotubes (CNT), using both first-principles density functional theory (DFT) and classical molecular dynamics methods. For the energetics, the van der Waals corrected DFT-D2 method was used to determine the stable adsorption sites and adsorption energies. In the (6,6) CNT/pyrene system, the adsorption energy was determined to be 0.73 eV by DFT-D2, in comparison to the result of 0.46 eV within local density approximation. This has shown that it is hard to peel pyrene from CNT at room temperatures. On the other hand, finite-temperature nonequilibrium molecular dynamics simulation has revealed that following the temperature gradient the pyrene molecule can readily move along the CNT sidewall, indicating that it is plausible to peel pyrene when it has moved to the end of the CNT. We have also studied the effect of pyrene adsorption on the thermal conductivity of CNT.