The present invention provides a hydrogenated polycyclic norbornene ring-opening polymer which is excellent in heat resistance, optical characteristics and processability which comprises recurring units represented by the following formula [I] and [II] or these recurring units substituted with alkyl in an amount of at least 10 mol % based on total polymer units and has an intrinsic viscosity [.eta.] of 0.01-20 dl/g measured in toluene at 25.degree. C., with at least 50% of C--C bonds which constitute main chain being single bonds: ##STR1## wherein --denotes a double bond or a single bond.