A method of producing a polar group-containing olefin copolymer through copolymerization of at least one nonpolar monomer selected from ethylene and α-olefins having from 3 to 20 carbon atoms, and at least one polar group-containing monomer containing a carboxyl group or a dicarboxylic acid anhydride group, in the presence of a transition metal catalyst, wherein the polar group-containing olefin copolymer is a random copolymer and satisfies the following requirements 1) to 3): 1) The amount of structural unit derived from the polar group-containing monomer in the polar group-containing olefin copolymer is from 0.001 to 10 mol%; and 2) The weight-average molecular weight (Mw) of the copolymer, as obtained through gel permeation chromatography, is from 45,000 to 1,000,000; and 3) The melting point, as represented by a temperature at a position of maximum peak in the absorption curve measured with a differential scanning calorimeter, is from 50°C to 140°C; wherein the transition metal catalyst is a transition metal catalyst represented by the following structural formula and/or and containing a chelating ligand and a metal of Groups 5 to 11: wherein M represents the above-mentioned transition metal; X 1 represents an oxygen atom; Y 1 represents carbon or silicon; n indicates an integer of 0 or 1; E 1 represents phosphorus, arsenic or antimony; R 3 and R 4 each independently represent a hydrogen atom or a hydrocarbon group having from 1 to 30 carbon atoms and optionally containing a hetero atom; R 5 each independently represents a hydrogen atom, a halogen atom, or a hydrocarbon group having from 1 to 30 carbon atoms and optionally containing a hetero atom; R 6 and R 7 each independently represent a hydrogen atom, a halogen atom, a hydrocarbon group having from 1 to 30 carbon atoms and optionally containing a hetero atom, OR 2, CO 2 R 2, CO 2 M', C N(R 1) 2, C R 2, SR 2, SO 2 R 2, SOR 2, OSO 2 R 2, P (OR 2) 2-y (R 1) y, CN, NHR 2, N(R 2) 2, Si(OR 1) 3-x (R 1) x, OSi(OR 1) 3-x (R 1) x, NO 2, SO 3 M', PO 3 M' 2, P (OR 2) 2 M' or an epoxy-containing group; M' represents an alkali metal, an alkaline earth metal, ammonium, a quaternary ammonium or phosphonium; x indicates an integer of from 0 to 3, y indicates an integer of from 0 to 2; R 6 and R 7 may bond to each other to form an alicyclic ring, an aromatic ring, or a hetero ring containing a hetero atom selected from oxygen, nitrogen and sulfur and the number of the ring-constituting atoms is from 5 to 8, and the ring may have or may not have a substituent thereon; R 1 represents a hydrogen atom, or a hydrocarbon group having from 1 to 20 carbon atoms; R 2 represents a hydrocarbon group having from 1 to 20 carbon atoms; L 1 represents a ligand coordinating with M; and R 3 and L 1 may bond to each other to form a ring. 1) The amount of structural unit derived from the polar group-containing monomer in the polar group-containing olefin copolymer is from 0.001 to 10 mol%; and 2) The weight-average molecular weight (Mw) of the copolymer, as obtained through gel permeation chromatography, is from 45,000 to 1,000,000; and 3) The melting point, as represented by a temperature at a position of maximum peak in the absorption curve measured with a differential scanning calorimeter, is from 50°C to 140°C;