The polymerization of a new polar diene-based monomer 2-(2-methylidenebut-3-enyl)furan (MBEF) without masking is achieved by using the bis(phosphino)carbazoleide-ligated yttrium (Y) alkyl complex upon the activation of [Ph3C][B(C6F5)4]. Under mild conditions, the polymerizations under the monomer-to-Y ratios ranging from 100:1 to 500:1 perform fluently in high yields. The afforded polydienes bearing pendant terminal furan groups have high cis-1,4-regularity up to 98.6% and molecular weights close to the theoretic values and narrow polymer dispersity index(PDI) (1.13–1.17) suggesting a livingness polymerization mode. In addition, this novel polydiene is an excellent building block for preparing functional rubber materials. For example, via Diels–Alder addition of furan groups under mild conditions, hydroxyl groups are successfully introduced on the side chains efficiently in a 75% conversion. Furthermore, the copolymerization of polar MBEF and nonpolar isoprene is also successfully realized by the bis(phosphino) carbazoleide-ligated scandium analog to access furan-modified cis-1,4 (>97%) polyisoprene with different MBEF contents (5.3%, 8.7%).