In the present research, a polymer, derived from the natural cellulose, grafted graphene oxide (CCG) bio-nanocomposite was prepared, and its efficiency as a targeted carrier was measured for loading curcumin, i.e., an anti-cancer drug. The structural and surface properties of CCG were examined using FESEM, BET, and FTIR techniques. In this research, Response Surface Method (RSM) along with the central composite design was employed to optimize the parameters such as the pH, contact time, and initial drug concentration, all affecting the drug adsorption on the composite. The central composite design results indicated that a second-order equation can properly fit the experimental data with a coefficient of determination of 0.9845 and p < 0.0001. The maximum adsorption (70 %) was achieved at pH = 6, contact time of 60 min, and initial concentration of 20 mg L⁻¹. The drug release from the CUR@CCG nanocarrier at pH = 5.6 was significantly higher than that at pH = 7.4, demonstrating the effectiveness of the system in the cancer cell environment. The MTT assay was conducted to assess the cytotoxicity of CUR, CCG, and CUR@CCG on two cell lines including the normal (MCF 10A) and breast cancer (MDA-MB 231). The cytotoxicity of CUR@CCG at the concentration of 96 μg mL⁻¹ for 24 h on MDA-MB 231 was almost 45 %, slightly lower than the free CUR (50 %). According to these results, the CCG bio-nanocomposite can be utilized as a biocompatible nanocarrier for targeted delivery of the CUR anti-cancer agent.