The invention relates to a tower (1) comprising a lower tubular tower section (2) made of concrete, an upper tubular tower section (3) made of steel and an adapter piece (7) for connecting the two tower sections (2, 3). The adapter piece (7) consists of an annular concrete element (8) and a steel element (9), the steel element (9) containing at least one annular flange (9a) that covers preferably entirely a surface of the concrete element (8), said surface being at the top in the installed state. The steel element (9) is directly cast together with the concrete element (8), wherein the annular flange (9a) is completely underpoured, essentially without air inclusions. In a method for producing a tower (1) comprising an adapter piece (7), a steel element (9) having an annular flange (9a) is placed head down into an annular formwork in order to produce said adapter piece (7). A concrete material is then introduced into the formwork in order to produce an annular concrete element (8) of the adapter piece (7), whereby the concrete material is directly applied onto the subsequent bottom side of the flange (9a).