To provide a polymerization method which polymerizes a cyclic monomer having two or more aliphatic unsaturated bonds in the molecular by using Fischer carbene complex, which has been considered that there has been no catalytic activity up to now and to provide its polymer.

The polymerization method of the cyclic monomer having two or more aliphatic unsaturated bonds is applied by Fischer carbene complex as a metathesis polymerization catalyst, further more this polymerization is carried out by the monomer having a metathesis reactive unsaturated bond and the polymer obtained by the above polymerization process.