A system (1) for feeding fuel from a tank (2) to an internal combustion engine (3) has: - an electrically actuated pre-feed variable-flow electric pump (9); - a high-pressure piston pump (10) having a pump casing (15) and piston movement mechanism (17) housed in the pump casing (16); and - a hydraulic circuit (7) comprising a first branch (11) for connecting the tank (2) to the pre-feed pump (9), a second branch (12) for connecting the pre-feed pump (9) to the high-pressure piston pump (10) and a third branch (13) for connecting the high-pressure piston pump (10) to the internal combustion engine (3); wherein the second branch (12) is configured to branch downstream of the pre-feed pump (9) into a first channel (12a) structured for conveying part of the fuel to the intake of the high-pressure piston pump (10) and for connecting the pre-feed pump (9) directly to the intake of the high-pressure piston pump (10), and into a second channel (12b) structured for conveying part of the fuel in the casing (15) and for connecting the pre-feed pump (9) to the casing (15) making the fuel flow solely through at least one calibrated hole (27).