Graphene-based materials modified with transition metals, and their potential utilization as hydrogen storage devices, are extensively studied in the last decades. Despite this widespread interest, a comprehensive understanding of the intricate interplay between graphene-based transition metal systems and H2 molecules remains incomplete. Beyond fundamental H2 adsorption, the activation of H2 molecule, crucial for catalytic reactions and hydrogenation processes, may occur on the transition metal center. In this study, binding modes of H2 molecules on the circumcoronene (CC) decorated with Cr or Fe atoms are investigated using the DFT methods. Side-on (η2-dihydrogen bond), end-on and dissociation modes of H2 binding are explored for high (HS) and low (LS) spin states. Spin state energetics, reaction energies, QTAIM and DOS analysis are considered. Our findings revealed that CC decorated with Cr (CC-Cr) emerges as a promising material for H2 storage, with the capacity to store up to three H2 molecules on a single Cr atom. End-on interaction in HS is preferred for the first two H2 molecules bound to CC-Cr, while the side-on LS is favored for three H2 molecules. In contrast, CC decorated with Fe (CC-Fe) demonstrates the capability to activate H2 through H–H bond cleavage, a process unaffected by the presence of other H2 molecules in the vicinity of the Fe atom, exclusively favoring the HS state. In summary, our study sheds light on the intriguing binding and activation properties of H2 molecules on graphene-based transition metal systems, offering valuable insights into their potential applications in hydrogen storage and catalysis.