  In the previous paper we developed a strong-coupling expansion for the
lattice QCD with the overlap fermions and showed that L\"usher's "extended"
chiral symmetry is spontaneously broken in some parameter region of the overlap
fermions. In this paper, we obtain a low-energy effective action and show that
there exist quasi-Nambu-Goldsone bosons which are identified as the pions. The
pion field is a {\em nonlocal} composite field of quark and anti-quark even at
the strong-coupling limit because of the nonlocality of the overlap fermion
formalism and L\"usher's chiral symmetry. The pions become massless in the
limit of the vanishing bare-quark mass as it is desired.
