  We develop a previously proposed gauge-invariant method to integrate out
infinite tower of Kaluza-Klein (KK) modes of vector and axialvector mesons in a
class of models of holographic QCD (HQCD). The HQCD is reduced by our method to
the chiral perturbation theory with the hidden local symmetry (HLS) having only
the lowest KK mode identified as the HLS gauge boson. We take the
Sakai-Sugimoto model as a concrete HQCD, and completely determine the ${\cal O}
(p^4)$ terms as well as the ${\cal O}(p^2)$ terms from the DBI part and the
anomaly-related (intrinsic parity odd) gauge-invariant terms from the CS part.
Effects of higher KK modes are fully included in these terms. To demonstrate
power of our method, we compute momentum-dependences of several form factors
such as the pion electromagnetic form factors, the $\pi^0$-$\gamma$ and
$\omega$-$\pi^0$ transition form factors compared with experiment, which was
not achieved before due to complication to handle infinite sums. We also study
other anomaly-related quantities like $\gamma^*$-$\pi^0$-$\pi^+$-$\pi^-$ and
$\omega$-$\pi^0$-$\pi^+$-$\pi^-$ vertex functions.
