The injection system (1) includes a pump (7) for supplying high-pressure fuel to a storage volume, defined for example by a common rail (6), for supplying a number of injectors (5). The pump (7) has at least one reciprocating pumping member (18) with a sinusoidal compression stroke (24). The injection system (1) includes at least one bypass solenoid valve (14) controlled by a control unit (16) having a chopper unit (28) for producing multiple deliveries (29, 31) at each compression stroke (24), so that the pressure in the common rail (6) is substantially level. Each pumping member (18) may be associated with a corresponding bypass solenoid valve (14).