Iron oxide nanoparticles, γ-Fe2O3NP, were deposited onto the surface of multi-walled carbon nanotubes and CNT/γ-Fe2O3NP hybrid nanomaterials were obtained. Then linear-dendritic ABA type block copolymers consisting of polyethylene glycol as B block and poly(citric acid) as A block, PCA–PEG–PCA, were synthesized and cisplatin (cis-diamminedichloroplatinum (CDDP)—a platinum-based chemotherapy drug) was conjugated with their carboxyl functional groups and CDDP/PCA–PEG–PCA anticancer prodrugs were prepared. Noncovalent interactions between CDDP/PCA–PEG–PCA anticancer prodrugs and CNT/γ-Fe2O3NP hybrid nanomaterials led to CDDP/PCA–PEG–PCA/CNT/γ-Fe2O3NP drug delivery systems. There are several key features of these hybrid drug delivery systems: (i) their ability to cross cell membranes and also high surface area per unit weight for high drug loading assigned to CNTs, (ii) high functionality, water solubility and biocompatibility assigned to PCA–PEG–PCA linear-dendritic copolymers and (iii) targeting tumors using a magnetic field assigned to γ-Fe2O3 nanoparticles. The efficacy of drug delivery systems for killing the cancer cells and targeting the drugs towards tumors was investigated.