In a high pressure fuel pump control apparatus for an internal combustion engine which has a high pressure fuel pump of an engine driven type capable of pressure feeding a controlled amount of fuel by driving a fuel suction valve to close at predetermined timing in a fuel delivery stroke, fuel pressure in an accumulator is swiftly raised by reliably pressure feeding a maximum amount of fuel from a fuel delivery stroke immediately after engine starting while avoiding heat generation by a solenoid for controlling the fuel suction valve, whereby deterioration of a combustion state and exhaust emissions at engine starting can be prevented. A starting time control section continuously energizes the solenoid over a period from the beginning of engine starting until when it becomes possible to perform valve closing timing control on the fuel suction valve based on the rotational position of the engine after completion of cylinder identification.