A control device comprising: a fuel injection control section for controlling an injector, which injects fuel stored in a fuel rail which stores fuel pressure-fed from a high-pressure pump, wherein said fuel injection control section comprises: homo-elasticity coefficient calculation means for calculating a homo-elasticity coefficient K from the equation K = V*dP/Xi, where V is a fuel rail volume, dP is the difference between the fuel pressure in the fuel rail measured before a fuel discharge from the high-pressure pump and the fuel pressure in the fuel rail measured after the fuel discharge from the high-pressure pump, and Xi is a pump discharge amount, fuel pressure estimation means for estimating pressure within the fuel rail in accordance with the homo-elasticity coefficient, and fuel control means for calculating an injector pulse width in accordance with the pressure estimated by said fuel pressure estimation means and outputting an injector drive pulse to the injector in accordance with the calculated injector pulse width, and wherein said homo-elasticity coefficient calculation means estimates the homo-elasticity coefficient K in consideration of a leak amount during an engine cranking period and in a low engine speed region prevailing before complete explosion in an engine which coordinates with a cam for driving the high-pressure pump, wherein the leak amount is fuel leaking from a gap in a pump plunger of the high-pressure pump. a fuel injection control section for controlling an injector, which injects fuel stored in a fuel rail which stores fuel pressure-fed from a high-pressure pump, wherein said fuel injection control section comprises: homo-elasticity coefficient calculation means for calculating a homo-elasticity coefficient K from the equation K = V*dP/Xi, where V is a fuel rail volume, dP is the difference between the fuel pressure in the fuel rail measured before a fuel discharge from the high-pressure pump and the fuel pressure in the fuel rail measured after the fuel discharge from the high-pressure pump, and Xi is a pump discharge amount, fuel pressure estimation means for estimating pressure within the fuel rail in accordance with the homo-elasticity coefficient, and fuel control means for calculating an injector pulse width in accordance with the pressure estimated by said fuel pressure estimation means and outputting an injector drive pulse to the injector in accordance with the calculated injector pulse width, and homo-elasticity coefficient calculation means for calculating a homo-elasticity coefficient K from the equation K = V*dP/Xi, where V is a fuel rail volume, dP is the difference between the fuel pressure in the fuel rail measured before a fuel discharge from the high-pressure pump and the fuel pressure in the fuel rail measured after the fuel discharge from the high-pressure pump, and Xi is a pump discharge amount, fuel pressure estimation means for estimating pressure within the fuel rail in accordance with the homo-elasticity coefficient, and fuel control means for calculating an injector pulse width in accordance with the pressure estimated by said fuel pressure estimation means and outputting an injector drive pulse to the injector in accordance with the calculated injector pulse width, and wherein said homo-elasticity coefficient calculation means estimates the homo-elasticity coefficient K in consideration of a leak amount during an engine cranking period and in a low engine speed region prevailing before complete explosion in an engine which coordinates with a cam for driving the high-pressure pump, wherein the leak amount is fuel leaking from a gap in a pump plunger of the high-pressure pump.