In this study, the PEG-Glu-Lys-Glu copolymer drug delivery system (GO/PEG-Glu-Lys-Glu) is prepared using glutamate-lysine-glutamate (Glu-Lys-Glu) modified polyethylene glycol (PEG) and connected graphene oxide nanosheets (GO). The multiple carboxyl groups of Glu-Lys-Glu and π–π interactions of GO can increase drug loading rate, and the fluorescence characteristics of GO could monitor the distribution of drug-loading systems in cells and the uptake of cells without the need for external dyes. Paclitaxel (PTX) is loaded via reduction-responsive disulfide bonds as a model medicine to examine the drug delivery potential of GO/PEG-Glu-Lys-Glu. The results showed that the drug loading content of PEG-Glu-Lys-Glu and GO/PEG-Glu-Lys-Glu to PTX is 7.11% and 8.97%, and the loading efficiency is 71.05% and 89.68%, respectively. It’s speculated that the π–π interaction between GO and PTX improved the drug-loading capacity and efficiency of GO/PEG-Glu-Lys-Glu. In vitro, in a simulated drug release test, at 48 h, the release of PTX was 85.51% at pH 5.0, 65.12% and 38.32% at pH 6.5 and 7.4, respectively. The cytotoxicity assay results showed that GO/PEG-Glu-Lys-Glu cell inhibition rate to MCF-7 cells was 7.36% at 72 h. The cell inhibition rate of GO/PEG-Glu-Lys-Glu/PTX system at 72 h was 92%, equivalent to free PTX. Therefore, the GO/PEG-Glu-Lys-Glu drug delivery system has the characteristics of good biocompatibility and sustainable release of PTX, which is expected to be applied in the field of tumor therapy.