A coffee-making apparatus for making normal coffee has a steam boiler (7) for generating steam for making cappuccino. The coffee-making apparatus has only one water reservoir (1) for making the coffee and for filling the steam boiler. The boiler has a venting valve (12) for automatically venting the boiler when the boiler is filled with cold water from the water reservoir. The influx of cold water into the boiler causes a sensor (12) to cool down, thereby opening a vent opening. With this apparatus it is possible to make coffee and steam for a second time, directly after making a cup of coffee and steam for the first time.