High-pressure fuel supply system of internal combustion engine

A high-pressure fuel supply system of an internal combustion engine is provided which includes a high-pressure pump (7) driven by the engine and operable with a cycle consisting of an intake stroke and a discharge stroke. The high-pressure pump includes a valve (16) selectively placed in an open position to allow the fuel to be introduced into the pump and in a closed position to allow the fuel to be fed under pressure to a high-pressure portion located downstream of the high-pressure pump. In the fuel supply system, commands for closing the valve are generated to the high-pressure pump during starting of the engine before the cylinders are discriminated from each other, such that a period of the generated commands is shorter than a half of the cycle of operation of the high-pressure pump during starting of the engine. After starting of the engine, a duration of closing of the valve during the discharge stroke of the pump is controlled so that a regulated amount of the fuel is fed under pressure to the high-pressure portion.