The present invention provides a lubricating oil composition having excellent low temperature viscosity properties suitable for engine oils for automobiles and industries, gear oils, shock absorber oils, hydraulic fluids and it also provides a lubricating oil for internal-combustion engines formed from the composition. The lubricating oil composition comprises; a lubricating oil base (A) having a kinematic viscosity at 100° C. of 1 to 50 mm2/s and a viscosity index of not less than 80, an ethylene•propylene copolymer (B) having the following properties (B1) to (B4) such that (B1) the ethylene content is from 30 to 75% by weight, (B2) the intrinsic viscosity [η] is from 1.3 to 2.0 dl/g, (B3) the Mw/Mn is not more than 2.4 and (B4) the melting point as measured with DSC is not higher than 30° C., and optionally a pour point depressant (C).