We have made a quantitative calculation for the systematic evolution of the 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 the average B-band extinction at z approximately 0.5 is typically 0.1-0.2 mag larger than the present value, 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&parr0; approximately 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 that show 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 approximately 0.2 mag at z approximately 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 open and Lambda-dominated flat cosmologies from the current data.
