Epoxy adhesive joints are increasingly being used to bond structural components in automotive, marine, and aircraft bodies. However, poor fracture toughness energy and low resistance to crack growth in structural epoxy adhesives are important drawbacks of these adhesives. To overcome this challenge, this paper aims to investigate the influence of dispersing graphene nanoplatelets (GNPs) into Axson-Sika Adekit A 140-1 structural epoxy adhesive on the fracture behavior of aluminum-to-glass fiber-reinforced polymer composite joints under mode-I and mode-II fracture tests. Double cantilever beam (DCB) and end-notched flexure specimens were fabricated to perform mode-I and mode-II fracture tests. For each specimen, three specimen groups including neat and graphene nanoplatelet reinforced with 0.05 wt.%, 0.1 wt.%, and 0.2 wt.% were considered. Results revealed that, for both of mode-I and mode-II tests, the optimum fracture toughness energy was obtained by inserting 0.1 wt.% of nanoparticles. By addition of 0.05 wt.% and 0.1 wt.% of GNPs, mode-I fracture toughness energy was improved by 90% and 115% compared with neat DCB specimens, while mode-II energy release rate increased by 55% and 83%, respectively. Finally, debonded surfaces were examined using optical microscope and scanning electron microscopy in order to find failure patterns and microstructural reinforcing mechanisms.