A brush module (6) for a rotating grinding brush, said brush module comprising: an elongate body part (7); at least one abrasive cloth (9) protruding from the body part (7); a plurality of bristles (8) extending from the body part (7) essentially in the same direction as the abrasive cloth (9). The body part (7) is provided with an undercut, longitudinally extending guide (13), and at an edge the abrasive cloth (9) is provided with a protruding head (15) that is complementary with the undercut groove (13) to the effect that the undercut guide (13) and the protruding bead (15) constitute complementary mechanical interconnecting means for releasable mounting of the abrasive cloth (9) on the body part (7). The protruding bead (15) is provided on a holder (14) comprising two flaps (16, 17), between which an edge of the abrasive cloth (9) is securely clamped. Besides, use of such abrasive cloth (9) in a rotating grinding brush with or without brush module.