Complexes of carbon nanotubes (CNTs) and nucleic acids allow fully exploit the potential of the CNTs in nanoelectronic devices, both by a size-specific matching of the two components and by the possibility to anchor also non-polar CNTs on the polar substrates such as oxides. The wrapping CNTs by the nucleic acid molecules allow also a transfer of CNTs into water solutions and a performance for their radii and lengths separation using chromatographical methods. In the present work for the first time the stability and electronic properties of the associates of the single-walled carbon nanotubes wrapped by homopolymeric single-stranded DNA molecules (CNT@DNA) are studied using a dispersion corrected modification of quantum mechanical density-functional tight-binding method (DFTB). A phenomenological model of the CNT@DNA formation energy depending on the nanotube radii is developed, which shows that the decoration of a CNT by a few (not single) DNA chains leads to a high water solubility of CNT@DNA. Pyrimidine-based DNAs are found to be more effective to wrap the CNTs, whereas purine-based DNAs are in wrapping more sensitive to the change of radii. The densities-of-states of the CNT@DNA complexes are close to the superposition of those of the “free” components with some additional states below Fermi level. The band gap in a hybrid CNT@DNA system is determined by the competition between the Fermi levels of the “free” DNA and CNT. In a few specific cases (complexes of polycytosine-DNA and a chiral metallic CNT) a considerable charge transfer from the DNA to the CNT was observed, combined with an additional gain in the CNT@DNA formation energy.