We perform computer simulations to explore the suprastructures and their formation mechanism in the length-dependent assembly of a stiff polymer chain on the carbon nanotube surface. Three types of local conformations, that is, helical wrapping along the nanotube threadline, nonhelical loop, and straight extension along the nanotube, are identified in the very stiff polymer, depending on its length. It is revealed that the high elastic energy penalty and the large length of a long stiff polymer hinder its conformation transition on the nanotube, which impairs the match between the polymer beads and the structural details of the underlying nanotube surface and thereby weakens the polymer-nanotube interaction. A preferred chain length with an energy minimum is documented for the first time in the self-assemble of a stiff polymer at the nanotube interface. These data significantly advance our understanding of the superstructure formation by self-assembly of various chain-like molecules (e.g., polymer, surfactants, DNA, peptides, etc.) on carbon nanotube.