The CH4 adsorption performance of the Sc-modified 6,6,12-graphyne (Sc@6,6,12-GY) system has been investigated based on giant canonical Monte Carlo (GCMC) simulations and first-principles study. According to the GCMC simulation, the CH4 adsorption amount of Sc modified 6,6,12-GY can reach 72.21 wt.% at 233 K and 40 bar. The first-principles study reveals that the binding energy is maximum (-5.181 eV) when the Sc atom is modified in the central hole site of the rhombic acetylene ring of 6,6,12-GY, which exceeds the cohesive energy of the Sc atom (-3.9 eV). The Sc@6,6,12-GY can adsorb 42 CH4 molecules with an average adsorption energy of -0.178 eV and an adsorption capacity of 72.13wt.%, which exceeds the U.S. Department of Energy standard (50 wt.%) and corroborates with the results obtained from the GCMC, verifying the accuracy of the results. Sc atoms modulate the electronic structure of 6,6,12-graphene, and the Sc-modified 6,6,12-GY system is found to have good CH4 storage properties as a high-capacity CH4 storage material by analyzing the partial state of the density, charge transfer situation and charge differential density map of the substrate system.