The synthesis of DNA nanotubes is an important area in nanobiotechnology. Different methods to assemble DNA nanotubes have been reported, and control over the width of the nanotubes has been achieved by programmed subunits of DNA tiles. Here we report the self-assembly of DNA nanotubes with controllable diameters. The DNA nanotubes are formed by the self-organization of single-stranded DNAs, exhibiting appropriate complementarities that yield hexagon (small or large) and tetragon geometries. In the presence of rolling circle amplification strands, that exhibit partial complementarities to the edges of the hexagon- or tetragon-building units, non-bundled DNA nanotubes of controlled diameters can be formed. The formation of the DNA tubes, and the control over the diameters of the generated nanotubes, are attributed to the thermodynamically favoured unidirectional growth of the sheets of the respective subunits, followed subjected to the folding of sheets by elastic-energy penalties that are compensated by favoured binding energies.