The injection system comprises a pump designed to send fuel at high pressure to an accumulation volume, for example formed by a common rail, for supplying a plurality of injectors. The pump comprises at least one pumping element actuated with reciprocating motion with a compression stroke at a sinusoidal speed, in synchronism with each step of fuel injection. The injection system comprises at least one by-pass solenoid valve, which is controlled by a chopper control unit for modulating the delivery of the pumping element by varying both the instant of start and the instant of end of delivery during the compression stroke, in such a way that the delivery is synchronous with the injection phase.