To provide an industrially useful α-olefin•((meth)acrylic acid)-based olefin copolymer having both a high molecular weight and a high comonomer content, a catalyst component capable of realizing a production of two different kinds of α-olefin•((meth)acrylic acid)-based olefin copolymers, and a production process using the catalyst. An α-olefin•((meth)acrylic acid)-based olefin copolymer is produced by using a metal complex complexed with a ligand represented by the following formula (Y is phosphorus or arsenic) for a catalyst composition.