Research on biocompatible metal-organic frameworks (MOFs) has recently attracted much attention from researchers as drug delivery systems. In this study, for the first time, Cu MOFs grown on graphene oxide capped with magnetic hydroxyapatite (MOF Cu@GO/HAp-SiO2-Fe3O4), and then the surface of the resulting nanocomposites was modified with the l-lysine amino acid (Lys-MOF Cu@GO/HAp-SiO2-Fe3O4) to prepare a controlled and pH-sensitive nanocomposite for targeted delivery of doxorubicin (DOX) to MDA-MB-231 breast cancer cells and MCF-10A normal cells. Different techniques confirmed the successful preparation of the designed nanocomposites. The values of encapsulation efficiencies (EE%) for MOF Cu@GO/HAp-SiO2-Fe3O4 and Lys-MOF Cu@GO/HAp-SiO2-Fe3O4 was found to be 79.3 % and 96.5 %, respectively. The in vitro DOX release results showed that the Lys-MOF Cu@GO/HAp-SiO2-Fe3O4 has a more controlled release than that of MOF Cu@GO/HAp-SiO2-Fe3O4 due to the slow diffusion of the drug through the Lys shell. In addition, both nanocomposites showed a pH-response release behavior. The release mechanism of DOX by the designed nanocomposites also revealed that the Korsmeyer-Peppas model is the best model to describe the release of the drug. Furthermore, in vitro cytotoxicity investigation confirmed that the prepared MOF Cu@GO/HAp-SiO2-Fe3O4 and Lys-MOF Cu@GO/HAp-SiO2-Fe3O4 nanocomposite had good biocompatibility against MDA-MB-231 and MCF-10A cells. Whereas, DOX-MOF Cu@GO/HAp-SiO2-Fe3O4 and DOX-Lys-MOF Cu@GO/HAp-SiO2-Fe3O4 against MDA-MB-231 cells increased the cytotoxicity as a result of the targeting and controlled delivery of the DOX to the cancer cells. The in vitro antioxidant activity and hemolysis experiments revealed that the designed Lys-MOF Cu@GO/HAp-SiO2-Fe3O4 have excellent antioxidant activity and good haemocompatibility, respectively, as a suitable nanocomposites for drug applications. Therefore, it is suggested that the prepared nanocomposites can be good for biological applications.