The use of 'water-in-salt' electrolytes has considerably expanded the electrochemical window of aqueous lithium-ion batteries to 3 to 4 volts, making it possible to couple high-voltage cathodes with low-potential graphite anodes(1-4). However, the limited lithium intercalation capacities (less than 200 milliampere-hours per gram) of typical transition-metal-oxide cathodes(5,6) preclude higher energy densities. Partial(7,8) or exclusive(9) anionic redox reactions may achieve higher capacity, but at the expense of reversibility. Here we report a halogen conversion-intercalation chemistry in graphite that produces composite electrodes with a capacity of 243 milliampere-hours per gram (for the total weight of the electrode) at an average potential of 4.2 volts versus Li/Li+. Experimental characterization and modelling attribute this high specific capacity to a densely packed stage-I graphite intercalation compound, C-3.5[Br0.5Cl0.5], which can form reversibly in water-in-bisalt electrolyte. By coupling this cathode with a passivated graphite anode, we create a 4-volt-class aqueous Li-ion full cell with an energy density of 460 watt-hours per kilogram of total composite electrode and about 100 per cent Coulombic efficiency. This anion conversion-intercalation mechanism combines the high energy densities of the conversion reactions, the excellent reversibility of the intercalation mechanism and the improved safety of aqueous batteries.