Graphene, a two-dimensional nanomaterial, has become a hot spot of research at the interface of nanotechnology and biomedicine. In this study, the oxidized form of graphene, graphene oxide (GO), was functionalized with 6-armed polyethylene glycol (PEG), which rendered it stable and biocompatible in physiological solution. The successful synthesis of PEGylated graphene oxide (GO-PEG) nanocarrier with low toxicity was confirmed by UV–Vis spectroscopy, Fourier-transform infrared spectroscopy, atomic force microscopy, and thermogravimetric analysis. By dynamic light scattering (DLS), the size distribution of the nanoparticles were shown to be 60–200 nm. Furthermore, a complex by loading an aromatic anticancer compound, podophyllotoxin (PPT), onto GO-PEG (GO-PEG/PPT) via π–π stacking and hydrophobic interactions was investigated. It was demonstrated that GO-PEG/PPT showed remarkably high cytotoxicity compared to free PPT in both the human cervical adenocarcinoma HeLa cell line and human hepatoma SMMC-7721 cell line. The loading and delivery of anticancer drugs using this kind of graphene-based nanocarrier may find potential application in biomedicine.