  We construct a realization of the elliptic quantum algebra
$U_{q,p}(\hat{sl_N})$ for any given level $k$ in terms of free boson fields and
their twisted partners. It can be considered as the elliptic deformation of the
Wakimoto realization of the quantum affine algebra $U_{q}(\hat{sl_N})$. We also
construct a family of screening currents, which commute with the currents of
$U_{q,p}(\hat{sl_N})$ up to total q-differences. And we give explicit twisted
expressions for the type $I$ and the type $II$ vertex operators of
$U_{q,p}(\hat{sl_N})$ by twisting the known results of the type $I$ vertex
operators of the quantum affine algebra $U_{q}(\hat{sl_N})$ and the new results
of the type $II$ vertex operators of $U_{q}(\hat{sl_N})$ we obtained in this
paper.
