  The most iron-deficient stars in the Milky Way provide important
observational constraints on the nature of astrophysical objects that have
enriched the primordial gas with heavy elements from which these stars were
formed. Among them, the recently discovered iron-deficient star SMSS
J031300.36-670839.3 shows a remarkable chemical composition with non-detection
of iron ([Fe/H]$<-7.1$) and large enhancement of carbon and magnesium relative
to calcium. We investigate the supernova yields of metal-free (Population III)
stars to interpret the observed abundance pattern for this star. We report that
the high [C/Ca] and [C/Mg] ratios and upper limits determined for other
elemental abundances are well reproduced with the yields of core-collapse
supernovae (that have normal kinetic energies of explosion $E$ of
$E_{51}=E/10^{51}$erg$=1$) or hypernovae ($E_{51}\geq 10$) of the Population
III 25$M_{\odot}$ or 40$M_{\odot}$ stars. The best-fit model assumes that the
explosion of the Population III progenitor undergoes extensive matter mixing
and fallback, leaving behind a black hole remnant. In these models, Ca is
produced by static/explosive O burning and incomplete Si burning in the
Population III supernova/hypernova, in contrast to the suggestion that Ca is
originated from the hot CNO cycle during the presupernova evolution. Among the
five most iron-poor stars with [Fe/H]$<-4.5$, four carbon-enhanced stars are
consistent with the faint supernova models with the ejected mass of $^{56}$Ni
less than 10$^{-3}M_{\odot}$.
