In this work, magnetic graphene oxide (MG) based carrier with targeted drug delivery ability was synthesized. The ability of beta-cyclodextrin (A-CD) grafted magnetic graphene oxide nanocomposite (beta-CD-MG) was evaluated as a nanocarrier for the delivery of doxorubicin (DOX) and methotrexate (MTX) as hydrophilic and hydrophobic anticancer drugs, respectively. The structural properties of the beta-CD-MG were explored using Fourier transform infrared (FT-IR), powder X-ray diffraction (XRD) and thermogravimetric analysis (TGA). Surface morphology and magnetic characteristic were investigated by using scanning electron microscopy (SEM), and vibrating sample magnetometer (VSM). The drug loading efficiency for the nanocomposite was obtained similar to 37.4% and similar to 23.4% for DOX and MTX, respectively. The obtained results showed that the nanocomposite in cancer cells conditions has a better drug release behavior than normal cells conditions. The Cellular toxicity tests suggested that nanocomposite with cell viability higher than 80% is nontoxic for K562. According to the findings results in this work, it could be concluded that beta-CD-MG as a safe carrier has the potential to deliver cancer drugs to the targeted cancer cells.