To provide an additive which can effectively prevent mist from appearing by using a copolymer which contains specified amounts of structural units derived from specific compounds as the additive.

Mist appearance from an aqueous cooling lubricant is prevented by using a copolymer containing 0.01-2 wt.% structural units derived from a compound represented by formula I (e.g. acrylamide) and a compound represented by formula II (e.g. acrylamidesulfonic acid). The copolymer has a number average mol.wt. of 100,000-2,000,000 and contains 2-50 wt.% structural units represented by formula I and 50-98 wt.% structural units represented by formula II. The copolymer may contain 5-20 wt.% structural units derived from compounds represented by formula III and/or formula IV. The aqueous cooling lubricant can be prepared by compounding water, base materials, functional additives, 0.01-2 wt.% above-mentioned copolymer. In the formulas, R1 is H or 1-4C alkyl; R2 is 1-6C alkylene; Y is an alkali metal; R3 and R4 are each H or 1-6C alkyl; R5 and R6 are each 3-5C alkenyl; and R7 and R8 are each 1-4C alkyl.