The present invention is intended to obtain a viscosity modifier for a lubricating oil, by the use of which a lubricating oil composition of excellent low-temperature properties can be obtained, and to obtain a lubricating oil composition of excellent low-temperature properties containing the viscosity modifier. The viscosity modifier for a lubricating oil comprises an ethylene/propylene copolymer (A) having the properties: the density is in the range of 857 to 882 kg/m3, Mw is in the range of 80,000 to 400,000, Mw/Mn is not more than 2.3, and the density (D (kg/m3)) and the melting point (Tm (° C.)) satisfy the relation Tm≦1.247×D−1037; or comprises an ethylene/propylene copolymer (B) having the properties: the ethylene content is in the range of 70 to 79 wt %, Mw is not less than 80,000 and less than 250,000, Mw/Mn is not more than 2.3, Tm is in the range of 15 to 60° C., and the ethylene content (E (wt %)) and the melting point (Tm (° C.)) satisfy the relation 3.44×E−206≧Tm; or comprises an ethylene/propylene copolymer (C) having the properties: the ethylene content is in the range of 70 to 79 wt %, Mw is in the range of 250,000 to 400,000, Mw/Mn is not more than 2.3, Tm is in the range of 15 to 60° C., and the ethylene content (E (wt %)) and the melting point (Tm (° C.)) satisfy the relation 3.44×E−204≧Tm. The lubricating oil composition comprises the ethylene/propylene copolymer (A) (B) or (C), a lubricating oil base (D), and if necessary, a pour point depressant.