  We investigate the formation of dust grains in the ejecta of population III
supernovae including pair--instability supernovae, applying a theory of non--
steady state nucleation and grain growth. In the calculations, the time
evolution of gas temperature in theejecta, which strongly affects the number
density and size of newly formed grains, is calculated by solving the radiative
transfer equation taking account of the energy deposition of radio active
elements. Two extreme cases are considered for the mixing of elements in the
ejecta; unmixed and uniformly mixed cases within the He--core.
  The results of calculations are summarized as the followings; in the unmixed
ejecta, a variety of grain species condense, reflecting the difference of the
elemental composition at the formation site in the ejecta, otherwise only oxide
grains condense in the uniformly mixed ejecta. The average size of newly formed
grains spans the range of three orders of magnitude, depending on the grain
species and the formation condition, and the maximum radius is limited to less
than 1 $\mu$m, which does not depend on the progenitor mass. The size
distribution function summed up over all grain species is approximated by a
power--law formula whose index is -3.5 for the larger radius and -2.5 for the
smaller one; the radius at the crossover point ranges from 0.004 to 0.1 $\mu$m,
depending on the model of supernovae. The fraction of mass locked into dust
grains increases with increasing the progenitor mass; 2--5 % of the progenitor
mass for core collapse supernovae and 15--30 % for pair--instability supernovae
whose progenitor mass ranges from 140 to 260 $M_{\odot}$. Thus, if the very
massive stars populate the first generation stars, a large amount of dust
grains would be produced in the early universe.
