Single-walled carbon nanotubes (SWCNTs) in their pristine form have high thermal conductivity whose further improvement has attracted a lot of interest. Some theoretical studies have suggested that the thermal conductivity of a (10,10) SWCNT is dramatically enhanced by C60 fullerene encapsulation. However, recent experiments on SWCNT bundles show that fullerene encapsulation leads to a reduction rather than an increase in thermal conductivity. Here, we employ three different molecular dynamics methods to study the influence of C60 encapsulation on heat transport in a (10,10) SWCNT. All the three methods consistently predict a reduction of the thermal conductivity of (10,10) SWCNT upon C60 encapsulation by 20%−30%, in agreement with experimental results on bundles of SWCNTs. We demonstrate that there is a simulation artifact in the Green-Kubo method which gives anomalously large thermal conductivity from artificial convection. Our results show that the C60 molecules conduct little heat compared to the outer SWCNT and reduce the phonon mean free paths of the SWCNT by inducing extra phonon scattering. We also find that the thermal conductivity of a (10,10) SWCNT monotonically decreases with increasing filling ratio of C60 molecules.