The Quinoxalin-2(H)-one (QO) and its derivatives of 3-methylquinoxalin-2(1H)-one (MQO) and 3- aminoquinoxalin-2(1H)-one (AQO) electrode potentials were calculated in aqueous phase. For this purpose, the DFT/B3LYP method, with the 6-311G basis set was utilized. The calculated value of the redox potentials relative to SHE were 0.123 eV, 0.015 eV and -0.254 eV for QO, MQO and AQO respectively. The amino derivative is (-0.76 eV) negative reduction potential because of amino group is more electron donating group comparison of methyl group. Energies of the highest occupied molecular orbital (HOMO) and the energy of the lowest unoccupied molecular orbital (LUMO) of the studied compounds were calculated in gas phase and water. Both electron donor and electron acceptor substituents are effective in reducing the energy gap between HOMO and LUMO. In addition, chemical potential (μ), chemical hardness (η), global electrophilicity (ω) and dipole moments were calculated. From the results shows that, quinoxalin-2-one, the greater is the tendency of the oxidized form to get reduced by accepting electrons and the amino derivative of quinoxalin-2-one is, the greater is the tendency of the reduced form to get oxidized by donating electrons.