A common rail fuel injection apparatus for an engine is provided which is equipped with a rail pressure sensor working to measure the pressure of fuel in a common rail, fuel injectors, and a controller. When the operation state of the rail pressure sensor monitored to be unusual, the controller changes the value of electricity supplied to an actuator of one of the fuel injectors to induce a change in a preselected operation characteristic of the engine. Upon appearance of such a change, the controller estimates the value of the rail pressure using the changed value of the electricity and a physical property of balance among forces acting on a valve of one of the fuel injectors which has induced the change in operation characteristic of the engine. The estimated value of the rail pressure is used for subsequent injections of the fuel into the engine.