Novel Nano graft composite pharmaceuticals were created by a two-part reaction process; part 1: One mole of glycerol and three moles of phthalic anhydride were reacted to create synthesis graft nano co-polymer, which was then characterized using FT-IR, 1 H- NMR, AFM, and XRD techniques. Part two: To create a unique nano graft composite drug, this nano graft co-polymer was combined with two distinct drug types (Cefotaxime and Ceftriaxone). The resulting composite drugs were analyzed using FT-IR, 1 HNMR, and 13 C- NMR spectroscopies. Using the (Pyrx) program, molecular docking was investigated to find the binding location of the ligand of a protein containing amino acids. The HEp-12 cell line was used to study the effects of the composite drugs, and the results showed that these compounds were highly effective at preventing the spread of liver cancer cells, as evidenced by the significant drop in the percentage of these cells. The cytotoxicity of two new nano graft composite drugs with cefotaxime and ceftriaxone in HEp-12 cells was found to be 49.551 mu g/ml and 47.351 mu g/ml, respectively. It has been shown to be highly effective compared to many common treatments for HCC and intrinsic liver cancer, including surgery to remove part of the liver, liver transplantation and liver-directed therapies such as hepatic artery embolization and resection. They may also use several types of chemotherapy, chemoembolization, radiation therapy, radioembolization, immunotherapy and targeted therapy.