In a coolant supply apparatus for a grinding machine, a wheel unbalance prevention device is operated within the period from the switching to the closed state of a shut-off valve which is provided on a conduit connecting a coolant supply to a coolant nozzle, to the rotation stop of the grinding wheel and prevents the coolant remaining in a part of the conduit on the downstream side of the shut-off valve and in the coolant nozzle, from dropping on the grinding surface of the grinding wheel during the rotation stop of the grinding wheel. Thus, it can be prevented that the coolant locally penetrates into the grinding wheel to put the same out of balance.