A fuel injection system of a compression ignition internal combustion engine provided with a fuel injection valve that injects fuel directly into a cylinder of the internal combustion engine, in which sub fuel injection is executed multiple times by the fuel injection valve in addition to main fuel injection at a time earlier than the main fuel injection, wherein the system comprises: an electronic control unit that is configured to change the number of times of execution (ns) of sub fuel injection in one combustion cycle based on an operation range within which the operation state of said internal combustion engine falls so that the lower the engine load of said internal combustion engine is, and the lower the number of engine revolutions of said internal combustion engine is, the more the number of times of execution of sub fuel injection in one combustion cycle is increased; a common rail that supplies fuel to said fuel injection valve; and a pressure changing means for changing the pressure (Pr) in said common rail in accordance with the number of times of execution of sub fuel injection in one combustion cycle, wherein the lower the atmospheric pressure is, the lower the temperature of cooling water of said internal combustion engine is, or the lower the temperature of intake air of said internal combustion engine is, the more an operation range in which the number of times of execution of sub fuel injection in one combustion cycle is large is expanded to higher loads and higher revolutions, the system being characterized in that, if the number of times of execution of sub fuel injection in one combustion cycle is to be decreased by said electronic control unit, then said pressure changing means is configured to start changing the pressure in said common rail, and thereafter said electronic control unit is configured to start the decrease in the number of times of execution of sub fuel injection after a specific period has elapsed, wherein said specific period is determined to correspond to a response delay period beginning with the start of the changing of the pressure in said common rail and ending when said pressure changing means completes the changing of the pressure in said common rail to a target value corresponding to the decreased number of time of execution of sub fuel injection, and in that, if the number of times of execution of sub fuel injection in one combustion cycle is to be increased by said electronic control unit, then said electronic control unit is configured to start the increase in the number of times of execution of sub fuel injection at the same time when said pressure changing means starts changing the pressure in said common rail to a second target value corresponding to the increased number of times of execution of sub fuel injection. an electronic control unit that is configured to change the number of times of execution (ns) of sub fuel injection in one combustion cycle based on an operation range within which the operation state of said internal combustion engine falls so that the lower the engine load of said internal combustion engine is, and the lower the number of engine revolutions of said internal combustion engine is, the more the number of times of execution of sub fuel injection in one combustion cycle is increased; a common rail that supplies fuel to said fuel injection valve; and a pressure changing means for changing the pressure (Pr) in said common rail in accordance with the number of times of execution of sub fuel injection in one combustion cycle, wherein the lower the atmospheric pressure is, the lower the temperature of cooling water of said internal combustion engine is, or the lower the temperature of intake air of said internal combustion engine is, the more an operation range in which the number of times of execution of sub fuel injection in one combustion cycle is large is expanded to higher loads and higher revolutions, the system being characterized in that, if the number of times of execution of sub fuel injection in one combustion cycle is to be decreased by said electronic control unit, then said pressure changing means is configured to start changing the pressure in said common rail, and thereafter said electronic control unit is configured to start the decrease in the number of times of execution of sub fuel injection after a specific period has elapsed, wherein said specific period is determined to correspond to a response delay period beginning with the start of the changing of the pressure in said common rail and ending when said pressure changing means completes the changing of the pressure in said common rail to a target value corresponding to the decreased number of time of execution of sub fuel injection, and in that, if the number of times of execution of sub fuel injection in one combustion cycle is to be increased by said electronic control unit, then said electronic control unit is configured to start the increase in the number of times of execution of sub fuel injection at the same time when said pressure changing means starts changing the pressure in said common rail to a second target value corresponding to the increased number of times of execution of sub fuel injection.