PURPOSE: To obtain a high-melting point cyclopolymer with small amounts of catalyst residue without the need for using any catalyst such as an organoaluminum compound in high yield, by catalytically polymerizing a specific hexadiene in the presence of a catalyst containing a specific metallocene compound.

CONSTITUTION: This polymer of formula III is obtained by catalytically polymerizing 1,5-hexadiene in the presence of a catalyst containing a metallocene compound of formula I or II (R is H, a 1-5C hydrocarbon or a Si-contg. hydrocarbon; when R is not H, two of the Rs may be mutually bound at the respective ω- terminals into a ring condensed with the cyclopentadiene ring; M is a group IIIA element with an atomic number of 21-71; X is H, a 1-10C hydrocarbon or a Si-contg. hydrocarbon; (m) is 0 or 1; Z is a 1-3C alkylene or alkylsilylene; D is a solvent molecule; (n) is 0-3). It is preferable that the metallocene compound be e.g. biscyclopentadienylsamarium.