A grinding attachment for use with a coffee machine an upper grinding tool arranged inside a casing, and a lower grinding tool (11), which can be rotated rotatable relative to the upper grinding tool during a grinding operation. An adjustment device adjusts a degree of grinding of a material to be ground with the grinding tools. The upper grinding tool is attached to a support. The support for the upper grinding tool is displaceable in the vertical direction and is secured torque-proof on an element of the adjustment device. The adjustment device comprises a guide for the support which, during the rotating of the adjustment element, moves the support together with the upper grinding tool in the vertical direction for adjusting the grinding gap.