In this work, for the first time, we conducted in-depth theoretical studies on the non-covalent complexes formed by cyclocarbons of different sizes and the most representative C60 fullerene, in order to reveal the structure, binding strength, and interaction nature of them. By means of high-precision density functional calculations, we found that the binding energy between cyclocarbons and C60 fullerenes is more than -14.4 kcal/mol, which is much stronger than that of C18 dimer and C60 fullerene dimer, suggesting the particularly strong affinity between cyclocarbon and fullerene.