  It has recently been suggested that the formation of horizon-size primordial
black hole (PBH) from pre-existing density fluctuations is effective during the
cosmic QCD phase transition.
  In this Letter we discuss the dependence of PBH formation on effective
relativistic degrees of freedom, $g_{\rm eff}$ during the cosmic QCD phase
transition.
  Our finding is important in the light of recent cosmological arguments of
several new classes of cosmic energy that appear from universal neutrino
degeneracy, quintessential inflation, and dark radiation in brane world
cosmology. Extra-energy component from the standard value in these new
cosmological theories is represented as an effective radiation in terms of
$g_{\rm eff}$. We conclude that the PBH formation during QCD phase transition
becomes more efficient if negative extra-component of the cosmic energy is
allowed because of the increase of the duration of the QCD phase transition,
which leads to smaller mass scale of PBHs. This suggests larger probability of
finding more PBHs if the dark radiation exists as allowed in the brane world
cosmology.
