To provide a friction modifier for lubricant, exhibiting decrease of shock in change gear and improved torque transmitting function, and to provide a lubricant composition containing the modifier.

The friction modifier for lubricant comprises an oil-soluble copolymer (A) containing at least one monomer (a) unit represented by general formula (1); CH2=C(R1)-Q-(Z-A1)m-X, and at least one monomer (b) unit represented by general formula (2); CH2=C(R3)-CO-(O-A2)n-OR4, and having ≥3,000 weight-average molecular weight. The friction modifier composition comprises the copolymer (A), and one or more selected from a group consisting of diluents and other additives. The lubricant composition comprises a base oil and the friction modifier or the friction modifier composition, wherein the composition contains 0.01-40 wt.% copolymer (A) based on the weight of the base oil.