To enhance the dispersion of graphene oxide (GO) in Styrene-butadiene-styrene (SBS) modified asphalt (SA) and the comprehensive physical properties of GO/SBS-modified asphalt (GSA), PEA-GO composites were prepared by grafting polyetheramine (PEA) onto GO for the preparation of PEA-GO/SBS-modified asphalt (PGSA). In this study, the chemical structure of PEA-GO was examined using fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS). The conventional properties of GSA and PGSA were analyzed. The effects of GO and PEA-GO on the high and low-temperature prevalent properties of SA were investigated by dynamic shear rheology (DSR) test and bending beam rheology (BBR) test. The adhesion properties of GSA and PGSA were investigated by surface free energy theory (SFE). The surface micro-morphology of GSA and PGSA and the dispersion state of GO in SA were analyzed using atomic force microscopy (AFM) and fluorescence microscopy (FM). The results showed that the characteristic absorption peaks of N-H, CH2-CH2, and C-N appeared in the FTIR diagram of PEA-GO. A new peak appeared in the XPS diagram: C-N. The high-temperature performance, low-temperature crack resistance, and adhesion of PGSA were superior to those of GSA. The size of the "bee structure" in PGSA is larger than in GSA, and PEA-GO demonstrates uniform dispersion in SA. This study serves as a reference for fine-tuning graphene oxide (GO) at the microscopic level to enhance the physical properties of GSA.