An energy storage system for a motor vehicle is provided, including an electric machine, which can be operated at least as a generator, for generating a generator current; a vehicle electrical system battery, which is connected to the electric machine in parallel; a capacitor unit, which is connected to the electric machine in parallel; and a controller for controlling the electric machine. The controller is configured such that if the vehicle is in the boost or braking operating mode, the battery of the vehicle electrical system is charged with a maximum battery charging current, whereas in all other cases the battery of the vehicle electrical system is charged by a battery charging current that is adjusted as a function of the charge state of the battery of the vehicle electrical system. Therefore, in order to adjust the battery charging current as a function of the charge state of the battery of the vehicle electrical system, three different charge states are considered.