The coffee maker comprises a height adjustment assembly by means of which the height position of a collecting tray, adapted to receive one or two coffee cups to be filled with coffee beverage, is adjustable. The collecting tray is attached to a support member. The height adjustment assembly comprises at least one vertically extending gear rack that can be non-positively engaged by a slider provided at the support member. The slider is biased by a spring towards the gear rack and can be manually displaced against the force of the spring.