The topological effect on thermal conductivity is investigated through the comparison among graphene nanoribbons, carbon nanorings, and the Möbius-like graphene strips (MGS) by molecular dynamics simulation. It is found that the thermal conductivity of MGS is less than one half of that of graphene nanoribbons. The underlying mechanism whereby MGS acquire such low thermal conductivity may be attributable to the enhanced phonon-phonon scattering and localization property, which are induced by the nontrivial topology of Möbius strip. Moreover, by counting in the dimensions of MGS, a lower length/width ratio reduces its thermal conductivity, as the phonon-phonon scattering and localization within might be further elevated.