New hybrid nanostructure-based magnetic drug delivery systems (HNMDDSs) consisting of carbon nanotubes, magnetic iron oxide nanoparticles, and linear-dendritic copolymers linked to anticancer drugs were synthesized and characterized. Polyamidoamine–polyethylene glycol–polyamidoamine (PAMAM–PEG–PAMAM) ABA type linear-dendritic copolymers were used to solubilize and functionalize carbon nanotubes through supramolecular chemistry. There are three key features of HNMDDSs: (a) use of functionalized MWCNTs as a biocompatible platform for the delivery of magnetic iron oxide nanoparticles, therapeutic drugs, and diagnostics, (b) use of PAMAM–PEG–PAMAM linear-dendritic copolymers as water soluble, biocompatible and high functional hybrid materials with a linear polyethylene glycol part which cause a high solubility for MWCNT through supramolecular interactions and dendritic PAMAM parts which cause a high functionality for MWCNT, (c) use of magnetic iron oxide nanoparticles as targeting, imaging, or hyperthermia cancer treatment agents. To prove the efficacy of synthesized HNMDDSs, they were subjected to the receptor-mediated endocytosis and release inside the cancer cells. Then, it was unambiguously proved that these tumor-targeting HNMDDSs are promising systems for future cancer therapy with low drug doses, thereby forming a solid foundation for further investigation and development.