Possibility of living metathesis polymerization by Mo catalysts was examined for (p-n-butyl-o,o,m,m-tetrafluorophenyl)acetylene, which has two fluorine atoms at both ortho positions. The MoOCl4-nBu(4)Sn-EtOH (1:1:1) catalyst yielded a polymer with narrow molecular weight distribution (($) over bar M(W)/($) over bar M(n) = 1.12), but the corresponding MoCl5-based catalyst did not formed such a polymer. With the former catalyst, the number-average molecular weight of polymer increased in direct proportion to monomer conversion, while the molecular weight distribution remained narrow; this proves the livingness of the polymerization. The optimal conditions for the living polymerization were [n-Bu(4)Sn]/[MoOCl4] = similar to 1.0, [EtOH]/[MoOCl4] = 0.5-1.5, and temperature less than or equal to 30 degrees C. n-Butyl acetate and acetone as well as EtOH were effective as third catalyst components.