  I study QCD at large isospin density, which is known to be in the superfluid
state with Cooper pairs carrying the same quantum number as pions. I solve the
gap equation derived from the perturbation theory up to the next-to-leading
order corrections. The pairing gap at large isospin chemical potential is found
to be enhanced compared to the color-superconducting gap at large baryon
chemical potential due to the $\sqrt{2}$ difference in the exponent arising
from the stronger attraction in one-gluon exchange in the singlet channel.
Then, using the gap function, I evaluate the contribution of the condensation
energy of the superfluid state to the QCD equation of state. At isospin
chemical potential of a few GeV, where the lattice QCD and the perturbative QCD
can be both applied, the effect of the condensation energy becomes dominant
even compared to the next-to-leading order corrections to the pressure in the
perturbation theory. It resolves the discrepancy between the recent lattice QCD
results and the perturbative QCD result.
