Surface characteristics of the gate-dielectric layers in graphene field-effect transistors (FETs) critically affect the electrical properties of the devices. In this report, the effects of self-assembled monolayers (SAMs) on the electrical properties of graphene FETs were examined by using various SAM buffer layers with different end groups and alkyl chain lengths. Especially, the dipole moment of the SAMs affects the doping properties of graphene as well as field-effect mobility, hysteresis, and stability of graphene FETs. The type and magnitude of doping are dependent on the functional groups in SAMs: Electron withdrawing fluorine groups p-dope the graphene whereas electron donating amine groups n-dope the graphene. The electrical stabilities such as hysteresis and gate-bias instability are mainly governed by the magnitude of the dipole moment in SAMs. Hexamethyldisilazane treatment resulted in graphene FETs with the highest electrical stabilities, because of the short one aliphatic alkyl chain with a negligible dipole moment. In contrast, in graphene FETs with SAMs having a strong dipole moment, electrical stabilities deteriorated by the charge trapping in SAMs.