  We have made a quantitative calculation for the systematic evolution of
average extinction by interstellar dust in host galaxies of high-redshift Type
Ia supernovae, by using a realistic model of photometric and chemical evolution
of galaxies and supernova rate histories in various galaxy types. We find that
average B band extinction <A_B> at z \sim 0.5 is typically 0.1-0.2 mag larger
than present, under a natural assumption that dust optical depth is
proportional to gas column density and gas metallicity. This systematic
evolution causes average reddening with E(B-V) \sim 0.025-0.05 mag with the
standard extinction curve, and this is comparable with the observational
uncertainty of the reddening of high-redshift supernovae. Therefore, our result
does not contradict the observations showing no significant reddening in high-z
supernovae. However, the difference in apparent magnitude between an open
universe and a \Lambda-dominated flat universe is only \sim 0.2 mag at z \sim
0.5, and hence this systematic evolution of extinction should be taken into
account in a reliable measurement of cosmological parameters. Considering this
uncertainty, we show that it is difficult to discriminate between an open and
\Lambda-dominated flat cosmologies from the current data.
