  The topology conserving gauge action proposed by Luescher is expected to
reduce the number of non-smooth gauge configurations as well as the topology
change compared to the conventional actions for the same lattice spacings. We
report our quenched QCD study of the topological stability and the scaling
violation of the static quark potential. We find that the the topology change
is indeed suppressed when the parameter epsilon is of order one. We also find
that the scaling violation in the static quark potential remain reasonably
small in the parameter range of our study. Our study is done at the inverse
lattice spacing a^{-1}=1.4-2.5 GeV with the lattice size L=1.0-1.6fm.
