It is well-known that Ru-based Grubbs catalysts undergo a highly selective alpha-addition to alkynes to promote exo-cyclization during ring-closing enyne metathesis (RCEYM) or to produce conjugated polyenes containing five-membered rings during the cyclopolymerization (CP) of 1,6-heptadiynes. There are a few reports of beta-selective addition to alkynes using Schrock catalysts based on Mo but none for readily accessible and easy-to-use Ru-based catalysts. We report the first example of beta-selective addition to alkynes using Grubbs Z-selective catalyst, which produces only endo products during the RCEYM reaction of terminal enynes and promotes the CP of 1,6-heptadiyne derivatives to give conjugated polyenes containing a six-membered ring as a major repeat unit. This unique preference for beta-selectivity originated from the side-bound approach of alkynes to the catalyst, where the steric hindrance between the chelating N-heterocyclic carbene ligand of the catalyst and the alkynes disfavored alpha-addition. To enhance the beta-selectivity for CP further, one could increase the size of the substrates on the monomers and lower the reaction temperature to obtain conjugated polyenes containing up to 95% six-membered rings. Moreover, the physical properties of the resulting polymer were analyzed in detail and compared with those of the conjugated polyenes containing only five-membered rings prepared from the same monomer but with a conventional Grubbs catalyst.