In this study, a nanocarrier was prepared for the codelivery of a hydrophilic drug (doxorubicin) and a hydrophobic drug (curcumin) to cancer cells. In this nanocarrier, the edges of graphene oxide sheets were decorated with a magnetic-functionalized polyamidoamine dendrimer with hydrazone groups at the end of the polymer. The edge functionalization of graphene sheets not only improved the solubility and dispersibility of graphene sheets but also imparted the magnetic properties to the nanocarrier. The resulting nanocarrier was loaded with doxorubicin through the covalent linkage and curcumin through π-π stacking. The nanocarrier showed a pH-sensitive release for both drugs, and the drug release behavior was also improved by the coimmobilization of both drugs. The cytotoxicity assay of nanocarrier showed low toxicity toward MCF-7 cell compared to unmodified graphene oxide, which was attributed to the presence of a magnetic dendrimer. Besides, the drug-loaded nanocarrier was highly toxic for cells even more than for free drugs. The cellular uptake images revealed higher drug internalization for coloaded nanocarrier than for the nanocarrier loaded with one drug alone. All of the results showed that the codelivery of curcumin and doxorubicin in the presence of the nanocarrier was more effective in chemotherapy than the nanocarrier loaded with one drug.