A new heteroleptic bis(phthalocyaninato)terbium(III) complex 1, bearing a pyrenyl group, exhibits temperature and frequency dependence of ac magnetic susceptibility, typical of single-molecule magnets. The complex was successfully attached to single-walled carbon nanotubes (SWNTs) using pi-pi interactions, yielding a 1-SWNT conjugate. The supramolecular grafting of 1 to SWNTs was proven qualitatively and quantitatively by high-resolution transmission electron microscopy, emission spectroscopy, and atomic force spectroscopy. Giving a clear magnetic fingerprint, the anisotropy energy barrier and the magnetic relaxation time of the 1-SWNT conjugate are both increased in comparison with the pure crystalline compound 1, likely due to the suppression of intermolecular interactions. The obtained results propose the 1-SWNT conjugate as a promising constituent unit in magnetic single-molecule measurements using molecular spintronics devices.