The invention relates to a vertical grinding mill, comprising a closed vertical milling container (1), in which a screw conveyor (2) is arranged so that it can be rotationally driven, conveying grinding bodies (17) to the top. The package of grinding bodies (17) adjusts itself during operation such that the surface (29) thereof is configured to slope radially outward and downward and to end in the region of the bottom edge (18) of an outlet for grinding material (11). Gas is introduced into the milling container (1) above the package of grinding bodies. The gas and grinding material (22) is removed from the milling container (1) via the outlet for grinding material (11).