  The non-relativistic $G_0 G$ formalism of BCS-BEC crossover at finite
temperature is extended to relativistic fermion systems. The uncondensed pairs
contribute a pseudogap to the fermion excitations. The theory recovers the BCS
mean field approximation at zero temperature and the non-relativistic results
in a proper limit. For massive fermions, when the coupling strength increases,
there exist two crossovers from the weak coupling BCS superfluid to the
non-relativistic BEC state and then to the relativistic BEC state. For color
superconductivity at moderate baryon density, the matter is in the BCS-BEC
crossover region, and the behavior of the pseudogap is quite similar to that
found in high temperature superconductors.
