The invention discloses a grinding tool fixing device with a damping function. The grinding tool fixing device comprises a connecting plate. First supporting rods are bonding to the right side of theend of the connecting plate. Second supporting rods are rotationally connected with the right sides of the first supporting rods through damping rotary shafts. A hydraulic shock absorber is movably connected with one end of the second supporting rod. One end of the hydraulic shock absorber is bonded to a hollow base. A fixing rod located between the two supporting rods is welded to the right sideof the connecting plate. A sliding plate is fixedly connected with the right side of the fixing rod. A base table is bonded to the inner wall of the hollow base. A first spring of which the right endis welded to the inner wall of the hollow base is matched with a gap of the end of the base table. A pin is fixedly connected with the left side of the first spring. According to the grinding tool fixing device with the damping function, when a grinding tool rotates to conduct cutting operation, impact force to the grinding tool can be buffered through certain displacement when the grinding tool just makes contact with objects needing to be ground, damage to the grinding tool is reduced, and the service life can be prolonged.