To obtain a viscosity index improver for making a low-temperature fluidity lower than that of a conventional polymethacrylate-based viscosity index improver.

This viscosity index improver comprises an oil-soluble polyalkylene ether (A) obtained by subjecting 290 pts.wt. of propylene oxide to addition polymerization to 1.8 pts.wt. of water and then subjecting 2,016 pts. wt. of butylene oxide to the addition polymer. The polyalkylene ether (A) has 18,800 number-average molecular weight, ≤8.67 solubility parameter, ≤-40°C crystallization starting temperature by a differential scanning calorimeter and 3.1 factor of steric hindrance.