The electrolyte solutions of 1 M LiBF4 dissolved in ethyl methyl carbonate (EMC)/sulfone mixtures are applied for dual-ion batteries using graphite positive electrodes. The representative sulfone solvents include sulfolane (SL) and 3-methylsulfolane, Graphite electrodes can deliver higher capacity of anion storage in the solutions of the mixed solvents than those of pure solvents. Traditional electrochemical and in situ X-ray diffraction measurements are performed on Li/graphite cells to probe the anion intercalation process at the interface between graphite electrode and electrolyte solutions. Ionic conductivity, viscosity, and NMR tests are carried out to characterize electrolyte solutions. The effects of ion-pairing between Li+ and BF4- and the anion solvations by EMC or sulfones on the anion storage in graphite have been addressed.