A common-rail fuel injection system is equipped with a common-rail, a fuel pump 11, and an injector. The fuel pump has a plurality of fuel pumping systems. A pressure sensor is provided at a fuel inlet of the injector. When the fuel pump supplies fuel to each of the fuel pumping systems, an ECU detects a variation in fuel pressure in a fuel passage between the fuel pump and the injector. Based on the detected fuel pressure variation, the ECU computes a pumping characteristic with respect to each of the fuel pumping systems.