To obtain an at least 3C olefinically unsaturated group-containing cycloolefin polymer excellent in transparency and dimensional stability upon being heated and desirable in the production of a polymer having terminal polar functional groups by adopting a specified process.

There is provided a cycloolefin polymer in which the cycloolefin polymer has a 3C or higher olefinic unsaturated group at least either terminal and which has a melt viscosity of below 0.25 dl/g as measured in decalin at 135°C according to DIN 53728 and comprises polymer units of at least one cycloolefin and, optionally, polymer units of at least one acyclic olefin. This polymer is obtained by adding a 3C or higher olefin in polymerizing a cycloolefin in the presence of a transition metal catalyst and a promoter. The amount of the 3C or higher olefin should be below 25 mol.% based on the total monomer weight. The polymer can be converted into various polar- functional-group-terminated polymer and block copolymers.