  Given a graph $H$ and an integer $p$, the {\it edge blow-up} of $H$, denoted
as $H^{p+1}$, is the graph obtained from replacing each edge in $H$ by a clique
of size $p+1$ where the new vertices of the cliques are all different. The
Tur\'{a}n numbers for edge blow-up of matchings were first studied by Erd\H{o}s
and Moon. In this paper, we determine the Tur\'{a}n numbers for edge blow-up of
general graphs.
