A process for producing a polar olefin copolymer comprising copolymerizing a non-polar olefin and a polar olefin in the presence of a catalyst comprising: (Al) a reaction product of and (A-i), wherein is a compound of the formula M'X k (c), wherein M' is a transition metal atom selected from Group 5 of the periodic table, k is a number satisfying the valence of M', and X is hydrogen, halogen, oxygen, a hydrocarbon group, a heterocyclic compound residual group, or a group containing O, S, N, B, Al, P, Si, Ge, Sn or halogen; if k is ≥ 2, the individual X may be the same or different, and plural groups X may be bonded to each other to form a ring; and (A-i) is a compound of the formula: wherein A is - O-, -S-, -Se- or -NR 6 -, and R 1 -R 6 each individually are selected from hydrogen, halogen, a hydrocarbon group, a heterocyclic compound residual group, and a group containing O, S, N, B, Al, P, Si, Ge or Sn, and two or more of them may be bonded to each other to form a ring; and at least one compound selected from: (B-1) an organometallic compound, (B-2) an organoaluminum oxy-compound, and (B-3) a compound which reacts with the reaction product (Al) to form an ion pair. (Al) a reaction product of and (A-i), wherein is a compound of the formula M'X k (c), wherein M' is a transition metal atom selected from Group 5 of the periodic table, k is a number satisfying the valence of M', and X is hydrogen, halogen, oxygen, a hydrocarbon group, a heterocyclic compound residual group, or a group containing O, S, N, B, Al, P, Si, Ge, Sn or halogen; if k is ≥ 2, the individual X may be the same or different, and plural groups X may be bonded to each other to form a ring; and (A-i) is a compound of the formula: wherein A is - O-, -S-, -Se- or -NR 6 -, and R 1 -R 6 each individually are selected from hydrogen, halogen, a hydrocarbon group, a heterocyclic compound residual group, and a group containing O, S, N, B, Al, P, Si, Ge or Sn, and two or more of them may be bonded to each other to form a ring; and is a compound of the formula M'X k (c), wherein M' is a transition metal atom selected from Group 5 of the periodic table, k is a number satisfying the valence of M', and X is hydrogen, halogen, oxygen, a hydrocarbon group, a heterocyclic compound residual group, or a group containing O, S, N, B, Al, P, Si, Ge, Sn or halogen; if k is ≥ 2, the individual X may be the same or different, and plural groups X may be bonded to each other to form a ring; and M' is a transition metal atom selected from Group 5 of the periodic table, k is a number satisfying the valence of M', and X is hydrogen, halogen, oxygen, a hydrocarbon group, a heterocyclic compound residual group, or a group containing O, S, N, B, Al, P, Si, Ge, Sn or halogen; (A-i) is a compound of the formula: wherein A is - O-, -S-, -Se- or -NR 6 -, and R 1 -R 6 each individually are selected from hydrogen, halogen, a hydrocarbon group, a heterocyclic compound residual group, and a group containing O, S, N, B, Al, P, Si, Ge or Sn, and two or more of them may be bonded to each other to form a ring; and A is - O-, -S-, -Se- or -NR 6 -, and R 1 -R 6 each individually are selected from hydrogen, halogen, a hydrocarbon group, a heterocyclic compound residual group, and a group containing O, S, N, B, Al, P, Si, Ge or Sn, and two or more of them may be bonded to each other to form a ring; and at least one compound selected from: (B-1) an organometallic compound, (B-2) an organoaluminum oxy-compound, and (B-3) a compound which reacts with the reaction product (Al) to form an ion pair. (B-1) an organometallic compound, (B-2) an organoaluminum oxy-compound, and (B-3) a compound which reacts with the reaction product (Al) to form an ion pair.