Polynorbornenes represent a fruitful class of polymers for structure–property study. Recently, vinyl-addition polynorbornenes bearing side groups of different natures were observed to exhibit excellent gas permeation ability, along with attractive C4H10/CH4 and CO2/N2 separation selectivities. However, to date, the gas transport properties of fluorinated addition polynorbornenes have not been reported. Herein, we synthesized addition polynorbornene with fluoroorganic substituents and executed a study on the gas transport properties of the polymer for the first time. A norbornene-type monomer with a C6F5 group, 3-pentafluorophenyl-exo-tricyclononene-7, was successfully involved in addition polymerization, resulting in soluble, high-molecular-weight products obtained in good or high yields. By varying the monomer concentration and monomer/catalyst ratio, it was possible to reach Mw values of (2.93–4.35) × 105. The molecular structure was confirmed by NMR and FTIR analysis. The contact angle with distilled water revealed the hydrophobic nature of the synthesized polymer as expected due to the presence of fluoroorganic side groups. A study of the permeability of various gases (He, H2, O2, N2, CO2, and CH4) through the prepared polymer disclosed a synergetic effect, which was achieved by the presence of both bulky perfluorinated side groups and rigid saturated main chains. Addition poly(3-pentafluorophenyl-exo-tricyclononene-7) was more permeable than its metathesis analogue by a factor of 7–21, or the similar polymer with flexible main chains, poly(pentafluorostyrene), in relation to the gases tested. Therefore, this investigation opens the door to fluorinated addition polynorbornenes as new potential polymeric materials for membrane gas separation.