The invention relates to a method for operating a fuel-supply system (1) for an internal combustion engine, said fuel-supply system (1) having a high-pressure fuel pump (3), a pressure-relief valve (5) and a high-pressure fluid accumulator (13), and the high-pressure fuel pump (3) being fluidically coupled on the outlet side to the pressure-relief valve (5) and to the high-pressure fluid accumulator (13). If the internal combustion engine is switched off, the high-pressure fuel pump (3) is controlled such that a pressure on the outlet side of the high-pressure fuel pump (3) is increased in such a way that the pressure-relief valve (5) is opened.