Three new phenylacetylene monomers having one or two carbamate groups were synthesized and polymerized by using (Rh(norbornadiene)Cl)2 as an initiator. The resulting polymers had very high average molecular weights (Mw) of 1.4–4.8 × 106, with different solubility and membrane-forming abilities. The polymer having two carbamate groups and no hydroxy groups in the monomer unit showed the best solubility and membrane-forming ability among the three polymers. In addition, the oxygen permeability coefficient of the membrane was more than 135 times higher than that of a polymer having no carbamate groups and two hydroxy groups in the monomer unit with maintaining similar oxygen permselectivity. A better performance in membrane-forming ability and oxygen permeability may be caused by a more extended and flexible cis-transoid conformation and lower polarity. On the other hand, the other two new polymers having one carbamate group and two hydroxy groups in the monomer unit showed lower performances in membrane-forming abilities and oxygen permeabilities. It may be caused by a very tight cis-cisoid conformation, which was maintained by intramolecular hydrogen bonds.