Porous graphene (PG) has a promising future in gas storage due to its unique pore characteristics and large specific surface area. The adsorption properties of PG and PG modified by Mn atoms (Mn-PG) for CH4 molecules have been studied based on first-principles density functional theory. It was found that the optimal adsorption position of CH4 on PG was the carbon annulus pore, and the adsorption energy was − 0.174 eV. The optimal position of the PG system modified by a single Mn atom is the central hole of the carbon ring, and the optimal position of the two Mn atoms is that Mn atoms are respectively located at different carbon ring holes on the opposite side of PG, with an average binding energy of -4.101 eV. The modification of Mn atom enhances the electronegativity of PG substrate and forms a negative charge center at the carbon ring, which is beneficial to enhance the adsorption performance of CH4 molecules with positive charge on the surface. The CH4 molecules are adsorbed on the PG surface through the electrostatic interaction with Mn atoms and PG substrates as well as the intermolecular force of CH4 molecules. Mn-PG system can adsorb 6 CH4 molecules on one side, and the average adsorption energy is -0.345 eV. When PG was modified with two Mn atoms, 12 CH4 molecules could be adsorbed on both sides, and the average adsorption energy was − 0.338 eV, the adsorption capacity can reach 38.43 wt.%.