  We show that the pseudogap of the quark density of states is formed in hot
quark matter as a precursory phenomenon of the color superconductivity on the
basis of a low-energy effective theory. We clarify that the soft mode of the
di-quark pair field gives rise to a peculiar behavior of the quark dispersion
relation and a short life-time of the quasiparticles near the Fermi surface,
both of which make a depression of the density of states of quarks. Our result
suggests that the appearance of the pseudogap is a universal phenomenon of
strong coupling superconductors, irrespective of the dimensionality.
