Provided are a viscosity modifier for lubricating oils for obtaining an additive composition for lubricating oils having excellent fluidity in a wide temperature range from low temperature to high temperature; and said additive composition for lubricating oils. Further provided are a viscosity modifier for lubricating oils for obtaining a lubricating oil composition capable of reducing viscosity in good balance in a wide temperature range from low temperature to high temperature; and said lubricating oil composition. The viscosity modifier for lubricating oils includes an ethylene α-olefin copolymer (A) which includes 30 to 50 mole % of structural units derived from at least one α-olefin selected from α-olefins having 4 and 5 carbon atoms and 50 to 70 mole % of structural units derived from ethylene (with the proviso that the total of all structural units of said copolymer is 100 mole %) and which satisfies specific requirements (a), (b), and (c).