Graphene is formed by a monolayer of cabon atoms linked together forming a hexagonal network. It has been extensively studied by researchers and attracted investment from various sectors of the economy, because it presents excellent mechanical, thermal, electrical and optical properties. The present work has as main objective the rheological characterization of the suspensions of graphene oxide (GO) dispersed in poly(ethylene) glycol (PEG 400), with different oxidation times (2 and 96 hours), through the use of rotational rheometry. Graphene oxide was obtained by Hummers method and characterized by various techniques. This method is based on the chemical exfoliation of graphite using strong acids such as sulfuric acid. Once the graphite oxide (GrO) is obtained, it is exfoliated in an ultrasonic bath in PEG to form the suspension with graphene oxide. The rheological characterization is fulfilled through measurements in steady shear flow, transient shear flow and oscillatory shear flow. The characterization of GO was performed using techniques such as: X-Ray Diffraction (XRD), Raman Spectroscopy, Fourier Transform Infrared (FTIR), Atomic Force Microscopy (AFM) and Thermogravimetric Analysis (TGA). The results will serve as a basis for understanding the interaction between the GO and the polymer, and the rheological behavior of GO-based polymer nanofluids.