The development of multifunctional nano-carriers with the ability of stimuli responsive controlled drug release can address many of the challenges of current cancer therapies. Graphene oxide (GO)-based nanomaterials with great specific surface area and oxygen-rich functional groups show desirable advantages for drug delivery systems. Therefore, in this research, GO sheets were functionalized by grafting hyperbranched polyglycerol- (HPG) through anionic ring-opening multi-branching polymerization (Anionic-ROMBP) of glycidol monomer. Then, magnetic nanoparticles (MNPs) were fabricated between the branches and on the surface of GO using the co-precipitation method (GO-HPG-MNPs). An anti-cancer model drug, curcumin (CUR), was loaded inside the nano-carrier via hydrophobic and π-π stacking interactions. After determining drug release pattern at weak acidic and physiological pH, the cytotoxicity of nano-carrier was investigated by MTT assay. FITC Annexin V/PI apoptosis detection kit was also applied to determine the method of cancer cells death. In addition to the in vitro studies, iATC-mISF bioinformatics server was used to predict the therapeutic and anatomical properties of CUR and its 75 derivatives. According to the results, GO-HPG-MNPs-(CUR) with negative surface charge (−49.4 mV) represented about 198% drug loading capacity and pH-responsive drug release. Results of MTT assay and flow cytometry confirmed cytotoxicity and apoptotic ability of GO-HPG-MNPs-(CUR) in cancer cells, while GO-HPG-MNPs (without drug) was biocompatible with no tangible toxicity. Moreover, for the first time, the conformity of MTT assay data and bioinformatics predictions exhibited the specific therapeutic/anatomical potential of CUR and about 51% of its derivatives on the nervous system. Thus, GO-HPG-MNPs-(CUR) can be suggested as a new type of functional nano-carrier in anti-cancer drug delivery and targeted cancer therapy.