  Let $\kappa'(G)$ be the edge connectivity of $G$ and $G\times H$ the direct
product of $G$ and $H$. Let $H$ be an arbitrary dense graph with minimal degree
$\delta(H)>|H|/2$. We prove that for any graph $G$, $\kappa'(G\times
H)=\textup{min}\{2\kappa'(G)e(H),\delta(G)\delta(H)\}$, where $e(H)$ denotes
the number of edges in $H$. In addition, the structure of minimum edge cuts is
described. As an application, we present a necessary and sufficient condition
for $G\times K_n(n\ge3)$ to be super edge connected.
