Enhancing thermopower is a key goal in organic and molecular thermoelectrics. Herein, it is shown that introducing noncovalent contact with a single-layer graphene (SLG) electrode improves the thermopower of saturated molecules as compared to the traditional gold-thiolate covalent contact. Thermoelectric junction measurements with a liquid-metal technique reveal that the value of Seebeck coefficient in large-area junctions based on n-alkylamine self-assembled monolayers (SAMs) on SLG is increased up to fivefold compared to the analogous junction based on n-alkanethiolate SAMs on gold. Experiments with Raman spectroscopy and field-effect transistor analysis indicate that such enhancements benefit from the creation of new in-gap states and electron doping through noncovalent interaction between the amine anchor and the SLG electrode, which leads to a reduced energy offset between the Fermi level and the transport channel. This work demonstrates that control of interfacial bonding nature in molecular junctions improves the Seebeck effect in saturated molecules.