A silicon-containing olefin copolymer is provided which comprises (a) a constituent unit derived from —CH₂—CH₂— such as ethylene, (b) a constituent unit derived from —CH₂—CHR— where R is a hydrocarbon group of 1 to 18 carbon atoms, and (c) a constituent unit containing a specific silicon-containing group. A silicon-containing olefin copolymer is also provided which is obtainable by co-polymerizing ethylene, an a-olefin of 3 to 20 carbon atoms and a specific silicon-containing ethylene monomer.