Disclosed is a process for producing an ethylene-α-olefin copolymer excellent in balancing between strength and elongation by continuous multi-step polymerization. The process comprises continuously polymerizing ethylene and α-olefin in a solvent in the presence of an olefin polymerization catalyst using a polymerization reaction apparatus comprising two or more tanks of polymerization reactors connected in series, said process including a first polymerization step of producing in one tank of polymerization reactor a polymer component under the polymerization condition of a flow state being 1.5 or more tanks in the perfect mixing cell model, and a second polymerization step of producing in one tank of polymerization reactor a polymer component under specific polymerization conditions.