A transmission fluid composition comprising: (i) a base oil which contains at least one of the following components and in a total amount of 10 to 100 mass% based on the mass of the base oil: a C16 to C56 α-olefin oligomer obtainable by dimerization of a C2 to C20 α-olefin in the presence of a metallocene catalyst to form an α-olefin dimer having a vinylidene bond, and dimerization of the α-olefin dimer in the presence of an acid catalyst, the C16 to C56 α-olefin oligomer being represented by the following formula or formula: R 1 -CH 2 -CH 2 -C(R 2)-CH-C(R 3) (CH 3)-CH 2 -CH 2 -R 4 R 1 -CH 2 -CH=C(R 2)-CH 2 -C(R 3) (CH 3)-CH 2 -CH 2 -R 4 wherein R 1 -R 4 each represent a hydrogen atom or a C 1-18 linear or branched alkyl group, and the total number of carbon atoms in R 1 -R 4 is 8-48; a hydrogenation product of the α-olefin oligomer, the hydrogenation product being represented by the following formula: R 1 -CH 2 -CH 2 -C(R 2)-CH 2 -C(R 3) (CH 3)-CH 2 -CH 2 -R 4 wherein R 1 -R 4 are as defined above for formulae and; and (ii) at least one component selected from an extreme-pressure agent, an oiliness agent, an antioxidant, a rust-preventive agent, a metal deactivator, a detergent dispersant, a viscosity index improver, a pour-point depressant and a defoamer. (i) a base oil which contains at least one of the following components and in a total amount of 10 to 100 mass% based on the mass of the base oil: a C16 to C56 α-olefin oligomer obtainable by dimerization of a C2 to C20 α-olefin in the presence of a metallocene catalyst to form an α-olefin dimer having a vinylidene bond, and dimerization of the α-olefin dimer in the presence of an acid catalyst, the C16 to C56 α-olefin oligomer being represented by the following formula or formula: R 1 -CH 2 -CH 2 -C(R 2)-CH-C(R 3) (CH 3)-CH 2 -CH 2 -R 4 R 1 -CH 2 -CH=C(R 2)-CH 2 -C(R 3) (CH 3)-CH 2 -CH 2 -R 4 wherein R 1 -R 4 each represent a hydrogen atom or a C 1-18 linear or branched alkyl group, and the total number of carbon atoms in R 1 -R 4 is 8-48; a hydrogenation product of the α-olefin oligomer, the hydrogenation product being represented by the following formula: R 1 -CH 2 -CH 2 -C(R 2)-CH 2 -C(R 3) (CH 3)-CH 2 -CH 2 -R 4 wherein R 1 -R 4 are as defined above for formulae and; and a C16 to C56 α-olefin oligomer obtainable by dimerization of a C2 to C20 α-olefin in the presence of a metallocene catalyst to form an α-olefin dimer having a vinylidene bond, and dimerization of the α-olefin dimer in the presence of an acid catalyst, the C16 to C56 α-olefin oligomer being represented by the following formula or formula: R 1 -CH 2 -CH 2 -C(R 2)-CH-C(R 3) (CH 3)-CH 2 -CH 2 -R 4 R 1 -CH 2 -CH=C(R 2)-CH 2 -C(R 3) (CH 3)-CH 2 -CH 2 -R 4 wherein R 1 -R 4 each represent a hydrogen atom or a C 1-18 linear or branched alkyl group, and the total number of carbon atoms in R 1 -R 4 is 8-48; a hydrogenation product of the α-olefin oligomer, the hydrogenation product being represented by the following formula: R 1 -CH 2 -CH 2 -C(R 2)-CH 2 -C(R 3) (CH 3)-CH 2 -CH 2 -R 4 wherein R 1 -R 4 are as defined above for formulae and; and (ii) at least one component selected from an extreme-pressure agent, an oiliness agent, an antioxidant, a rust-preventive agent, a metal deactivator, a detergent dispersant, a viscosity index improver, a pour-point depressant and a defoamer.