Described herein is an electronic-injection fuel-supply system (12) for an internal-combustion engine (1) having at least one injector (13) and a fuel pump (14); the fuel pump (14) is provided with: a variable-volume pumping chamber (20); a one-way intake valve (28); a one-way delivery valve (24); a mobile piston (21) that integrates within it the intake valve (28) and is coupled to the pumping chamber (20) to vary cyclically the volume of the pumping chamber (20) itself; and an actuator device (27) that impresses a reciprocating motion on the piston (21) and has an electromagnetic actuator (29) for actuating the piston (21) during an intake phase and a spring (30) for actuating the piston (21) during a delivery phase.