A fuel injection system (5) supplies fuel at a high pressure to an internal combustion engine (500) via at least two high-pressure fuel pumps (100, 200) and a high-pressure fuel distribution line system (300) fluidly communicating with the internal combustion engine (500). The high-pressure fuel pumps (100, 200) are configured to be operated in a first pump mode and a second pump mode, such that in the first pump mode a first amount of fuel (105, 205) is pumped, and in the second pump mode a second amount of fuel (105, 205) is pumped. A control unit (400) is configured to alternately operate the high- pressure fuel pumps (100, 200) such that, during a first time period at least one of the high-pressure fuel pumps (100, 200) is operated in the first pump mode and all other high-pressure fuel pumps (100, 200) are simultaneously operated in the second pump mode, and such that during a second time period at least one of the high-pressure fuel pumps (100, 200), which was/were operated in the first time period in the second pump mode, is operated in the first pump mode and the remaining high-pressure fuel pumps (100, 200) are simultaneously operated in the second pump mode.