Motivated by the discovery of extremely bright supernovae SNe 1999as and 2006gy, we have investigated how much 56Ni mass can be synthesized in core-collapse massive supernovae (SNe). We calculate the evolution of several very massive stars with initial masses M ≤ 100 M☉ from the main sequence to the beginning of the Fe core collapse and simulate their explosions and nucleosynthesis. In order to avoid complications associated with strong mass loss, we consider only metal-poor stars with initial metallicity Z = Z☉/200. However, our results are applicable to higher metallicity models with similar C+O core masses. The C+O core mass for the 100 M☉ model is MCO = 42.6 M☉, and this is the heaviest model in the literature for which Fe-core-collapse SN is explored. The synthesized 56Ni mass increases with the increasing explosion energy and progenitor mass. For the explosion energy of E51 ≡ E/1051 ergs = 30, for example, the 56Ni masses of M(56Ni) = 2.2, 2.3, 5.0, and 6.6 M☉ can be produced for the progenitors with initial masses of 30, 50, 80, and 100 M☉ (or C+O core masses MCO = 11.4, 19.3, 34.0, and 42.6 M☉), respectively. We find that producing M(56Ni) ~ 4 M☉ as seen in SN 1999as is possible for MCO 34 M☉ and E51 20. Producing M(56Ni) ~ 13 M☉, as suggested for SN 2006gy, requires a too large explosion energy for MCO 43 M☉, but it may be possible with a reasonable explosion energy if MCO 60 M☉.