Glassy graphene is obtained via molecular dynamics simulation, and we investigated the effect of cooling rates on the forming and mechanical properties of glassy graphene (GG). The system interactions are modeled using the adaptive intermolecular reactive bond order (AIREBO) potential. The results of our simulations are in good agreement with experimental ones in the case of crystalline graphene. We calculated the radial distribution function (RDF) to characterize the structural properties of the forming glass and used the Wendt-Abraham parameter to determine the glass temperature transition (Tg). As a result, we found that as the cooling rate increased, the rigidity of the glassy graphene decreased. The calculated Young's modulus equals 70.33 GPa, 29.76 GPa, 12.42 GPa, and 2.85 GPa for cooling rates equal to 0.1 K/ps, 1 K/ps, 10 K/ps, and 100 K/ps, respectively.