  We extend the work of Foda et al and propose an elliptic quantum algebra
$A_{q,p}(\hat {sl_n})$. Similar to the case of $A_{q,p}(\hat {sl_2})$, our
presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and
$R^*$ are $Z_n$ symmetric R-matrices with the elliptic moduli chosen
differently and a factor is also involved. With the help of the results
obtained by Asai et al, we realize type I and type II vertex operators in terms
of bosonic free fields for $Z_n$ symmetric Belavin model. We also give a
bosonization for the elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ at level
one.
