Disclosed is a cycloolefin copolymer composition (C) obtained by copolymerizing an .alpha.-olefin of two or more carbon atoms (a) and a specific cycloolefin (b) in the presence of an aromatic ring-containing vinyl hydrocarbon/conjugated diene copolymer or a product of hydrogenation thereof (A) which has an intrinsic viscosity (.eta.) of 0.5 to 5.0 dl/g; at least one glass transition temperature (measured by DSC) of lower than 15.degree. C.; polymerizable carbon-to-carbon double bonds in an amount of 2 to 150 in terms of iodine value; and a refractive index n.sub.D (A) of 1.50 to 1.65. In the composition (C), the component (A) is contained in an amount of 1 to 40% by weight, and a difference .DELTA.n.sub.D between the refractive index n.sub.D (A) of the component (A) and a refractive index n.sub.D (B) of a cycloolefin copolymer component (B) obtained by copolymerizing the .alpha.-olefin (a) and the cycloolefin (b) in the absence of the component (A) is not more than 0.015. The cycloolefin copolymer composition is excellent in impact resistance, transparency and heat resistance.