  Using self-consistent chemodynamical simulations including star formation,
supernova feedback, and chemical enrichment, I show the dependence of cosmic
star formation and chemical enrichment histories on the initial mass function
(IMF). The effects of Pop-III IMF can be only seen in the elemental abundance
ratios at z>4 or [Fe/H]<-2. The preferable IMF has a flatter slope in the case
of high star formation rate (SFR) and smaller upper-mass (~20Msun) in the case
of low SFR, which is consistent with the observed elemental abundances of dwarf
spheroidal galaxies. However, the [alpha/Fe] problem of elliptical galaxies may
require other solutions.
