A rapid charging circuit for a lithium ion battery. The battery charger in accordance with the present invention compensates for the voltage drops across the various resistance elements in the battery circuit by setting the charging voltage to a level to compensate for the initial resistance of the series resistances in the circuit and an additional resistance selected to take into account the anticipated increase in resistance of the various circuit elements over time. The battery charger in accordance with the present invention periodically monitors the open-circuit voltage of the battery cell and reduces the charging voltage to when the battery cell voltage reaches the optimal value. Thus, during a constant current charging mode, the battery cell is driven at a relatively optimal charging current to reduce the charging time. As such, the system is able to optimize the charging current supplied to a battery cell during a constant current mode of operation while compensating for circuit elements whose resistance may vary over time due to temperature or other factors, such as corrosion, while at the same time avoiding exceeding the maximum recommended voltage for the battery cell.