A transmission fluid composition comprising: 0.5 to 30 mass%, based on the total amount of the transmission fluid, of a viscosity index improver selected from a polymethacrylate, an olefin copolymer and a styrene copolymer; a base oil containing at least one of the following α-olefin oligomers and α-olefin oligomer hydrogenation products -; and optionally up to 50 mass% of an additional oil: a C16 to C40 α-olefin oligomer obtainable by oligomerization of a C2 to C20 α-olefin in the presence of a metallocene catalyst; a hydrogenation product of the α-olefin oligomer; 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; a hydrogenation product of the α-olefin oligomer; a C16 to C40 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 addition of a C6 to C8 α-olefin to the α-olefin dimer in the presence of an acid catalyst; and a hydrogenation product of the α-olefin oligomer; wherein the composition contains 50 mass % or more of at least one species selected from among the components to and the composition has a kinematic viscosity, as determined at 100°C, of 2 to 10 mm 2 /s, a viscosity index of 150 or higher, and a kinematic viscosity and NOACK evaporation loss satisfying the following formula: X / 3 + Y ≤ 6.33 wherein X represents the kinematic viscosity (mm 2 /s) at 100°C, and Y represents the NOACK evaporation loss (mass%) at 200°C over one hour. 0.5 to 30 mass%, based on the total amount of the transmission fluid, of a viscosity index improver selected from a polymethacrylate, an olefin copolymer and a styrene copolymer; a base oil containing at least one of the following α-olefin oligomers and α-olefin oligomer hydrogenation products -; and optionally up to 50 mass% of an additional oil: a C16 to C40 α-olefin oligomer obtainable by oligomerization of a C2 to C20 α-olefin in the presence of a metallocene catalyst; a hydrogenation product of the α-olefin oligomer; 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; a hydrogenation product of the α-olefin oligomer; a C16 to C40 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 addition of a C6 to C8 α-olefin to the α-olefin dimer in the presence of an acid catalyst; and a hydrogenation product of the α-olefin oligomer; a C16 to C40 α-olefin oligomer obtainable by oligomerization of a C2 to C20 α-olefin in the presence of a metallocene catalyst; a hydrogenation product of the α-olefin oligomer; 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; a hydrogenation product of the α-olefin oligomer; a C16 to C40 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 addition of a C6 to C8 α-olefin to the α-olefin dimer in the presence of an acid catalyst; and a hydrogenation product of the α-olefin oligomer;