  We have considered the holographic large $N_c$ QCD model proposed by Sakai
and Sugimoto and evaluated the non-Abelian DBI-action on the D8-brane upto
$(\alpha')^4$ terms. Restricting to the pion sector, these corrections give
rise to four derivative contact terms for the pion field. We derive the
Weinberg's phenemenological lagrangian. The coefficients of the four derivative
terms are determined in terms of $g_{YM}^2$. The low energy pion-pion
scattering amplitudes are evaluated. Numerical results are presented with the
choice of $M_{KK}=0.94 GeV$ and $N_c=11$. The results are compared with the
amplitudes calculated using the experimental phase shifts. The agreement with
the experimental data is found to be satisfactory.
