  This paper investigates the evolution of the dust-to-metal ratio in galaxies
based on a simple evolution model for the amount of metal and dust with infall.
We take into account grain formation in stellar mass-loss gas, grain growth by
the accretion of metallic atoms in a cold dense cloud, and grain destruction by
SNe shocks. Especially, we propose that the accretion efficiency is independent
of the star-formation history. This predicts various evolutionary tracks in the
metallicity ($Z$)--dust-to-gas ratio ($\cal D$) plane depending on the
star-formation history. In this framework, the observed linear $Z$--$\cal D$
relation of nearby spiral galaxies can be interpreted as a sequence of a
constant galactic age. We emphasize that an observational study of the
$Z$--$\cal D$ relation of galaxies at $z\sim 1$ is very useful to constrain the
efficiencies of dust growth and destruction. We also suggest that the
  Lyman break galaxies at $z\sim 3$ have a very low dust-to-metal ratio,
typically $\ltsim 0.1$. Although the effect of infall on the evolutionary
tracks in the $Z$--$\cal D$ plane is quite small, the dispersion of the infall
rate can disturb the $Z$--$\cal D$ relation with a constant galactic age.
