The thermodynamics and molecular structure of a supramolecular complex between a tubular molecule, (P)-(12,8)-cyclo-2,8-anthanthrenylene, and fullerene were investigated. The enthalpy-driven characteristics of the association were enhanced upon lengthening of the curved sp2-carbon networks in the tubular molecule as a result of an increase in the C–C contact areas in addition to the emergence of CH–π contacts with aliphatic chains. The involvement of CH–π interactions in the molecular recognition consequently increased the entropy cost for the association, and the importance of molecular structures at the edge of tubular molecules was revealed. An inflection-free, smooth surface inside the tubular molecule was revealed by crystallographic analysis, which allowed for dynamic motions of the encapsulated fullerene molecule in solution. This study provided a new example of a molecular peapod with a smoothly curved π-interface to be examined in the structure–thermodynamics relationship study and led to an in-depth understanding of peapods in general.