A method operates a fuel-supply system for an internal combustion engine. The fuel-supply system contains a high-pressure fuel pump, a high-pressure fluid accumulator having a fuel-injection valve, and a high-pressure sensor. A measurement signal of the sensor is representative of a pressure within the high-pressure fluid accumulator. The high-pressure fuel pump is fluidically connected on the outlet side to the high-pressure fluid accumulator. A respective maximum injection quantity of the fuel-injection valve is determined depending on the measurement signal of the high-pressure sensor. The injection quantity is determined depending on an efficiency characteristic representing the efficiency of the high-pressure fuel pump, the efficiency characteristic depending on the measurement signal of the high-pressure sensor. The at least one fuel-injection valve is actuated in such a way that a respective injection quantity to be metered by the at least one fuel-injection valve is limited to the respective maximum injection quantity.