A vertical grinding mill is provided including a closed vertical milling container in which a screw conveyor is arranged for rotary drive so as to convey grinding bodies to the top. The package of grinding bodies adjusts itself during operation such that the surface thereof is configured to slope radially outwards and downwards and to end in the region of the bottom edge of an outlet for grinding stock. Gas is introduced into the milling container above the package of grinding bodies. The gas and grinding stock are discharged from the milling container via the outlet for grinding stock.