The generalized $k$-connectivity of a graph $G$, denoted by $κ_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of the classical connectivity and plays a key role in applications related to the modern interconnection networks. The godan graph $EA_n$ is a kind of Cayley graphs which posses many desirable properties. In this paper, we shall study the generalized 4-connectivity of $EA_n$ and show that $κ_4(EA_n)=n-1$ for $n\ge 3$.