Uranium extraction has been widely studied for (i) the uranium recovery for nuclear fuel resource and nuclear waste management; and (ii) the uranium deficiency in geological deposits. Sorption is one of the most promising technologies for extracting uranium. To investigate effective sorption material, the ordered mesoporous carbon (CMK-3) was functionalized with phosphate ligands and amidoxime ligands. The phosphorylated CMK-3 and amidoximed CMK-3 were applied for sorption of U(VI) under highly acidic condition and seawater condition, respectively. Under highly acidic condition (1-2 M $HNO_3$), CMK-3-Bz-$PO_4$ exhibited the highest U(VI) sorption (10.6 mg/g) due to the electron donating effect of the benzene ring providing more negative charge toward phosphoryl oxygen which is the binding site for U(VI). On the other hand, in pH 1-4 range, CMK-3-Et-PO4 and CMK-3-Py-$PO_4$ had a conspicuous increase in sorption performance due to the electron withdrawing effects of ethyl amide and pyridine when enhancing the acidities of functional groups. CMK-3-An-AO exhibited a maximum U(VI) sorption capacity under seawater condition (170 $\mu$g/g) because the amine group onto An-AO improved the overall complexation between amidoxime and U(VI). Electron withdrawing effect of the amine group lowered the charge on U(VI) in the complex through hydrogen bonding with the water molecules surrounding U(VI). According to the findings of this work, the results provide a promising platform for the development of functionalized carbon sorbents for U(VI) extraction from spent nuclear fuels or seawater.