An injector for fuel includes a passage for receiving fuel at an above-atmospheric first pressure, a pressure amplifier and an injection valve which is settable in an open position and a closed position. The injection valve includes a piston element, a closing chamber and an opening chamber. To inject fuel, the pressure amplifier generates a higher second fuel pressure in the opening chamber so that the valve element moves towards an open position and fuel is injected. To end injection of fuel, the high pressure in the opening chamber is reduced and the closing chamber is connected to the fuel source at the first pressure so that the valve is moved towards the closed position by a combined force created by the first pressure and the spring.