  The perturbative pion form factor with Sudakov suppression is re-examined.
Taking into account the multi-gluon exchange in the law $Q^2$ regions, we
suggest that the running coupling constant should be frozen at
$\alpha_s(t=\sqrt{<{\bf k}_{T}^{2}>})$ and $\sqrt{<{\bf k}_{T}^{2}>}$ is the
average transverse momentum which can be determined by the pionic wave
function. In addition, we correct the previous calculations about the Sudakov
suppression factor which plays an important role in the perturbative
predictions for the pion form factor.
