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

Evolution of Very Massive Population III Stars with Mass Accretion from Pre-Main Sequence to Collapse