  We calculate the evolution of zero-metallicity Population III (Pop III) stars
whose mass grows from the initial mass of $\sim 1M_{\odot}$ by accreting the
surrounding gases. Our calculations cover a whole evolutionary stages from the
pre-main sequence, via various nuclear burning stages, through the final core
collapse or pair-creation instability phases. We adopt the following stellar
mass-dependent accretion rates which are derived from cosmological simulations
of early structure formation based on the low mass dark matter halos at
redshifts $z \sim 20$: (1) the accretion rates for the first generation (Pop
III.1) stars and (2) the rates for zero-metallicity but the second generation
(Pop III.2) stars which are affected by radiation from the Pop III.1 stars. For
comparison, we also study the evolution with the mass-dependent accretion rates
which are affected by radiatibe feedback. We show that the final mass of Pop
III.1 stars can be as large as $\sim 1000M_{\odot}$, beyond the mass range
($140 - 300M_{\odot}$) for the pair-instability supernovae. Such massive stars
undergo core-collapse to form intermediate-mass black holes, which may be the
seeds for merger trees to supermassive black holes. On the other hand, Pop
III.2 stars become less massive ($\lsim 40 - 60M_{\odot}$), being in the mass
range of ordinary iron core-collapse stars. Such stars explode and eject heavy
elements to contribute to chemical enrichment of the early universe as observed
in the abundance patterns of extremely metal-poor stars in the Galactic halo.
