  Let $S(G^\sigma)$ be the skew-adjacency matrix of an oriented graph
$G^\sigma$. The skew energy of $G^\sigma$ is defined as the sum of all singular
values of its skew-adjacency matrix $S(G^\sigma)$. In this paper, we first
deduce an integral formula for the skew energy of an oriented graph. Then we
determine all oriented graphs with minimal skew energy among all connected
oriented graphs on $n$ vertices with $m \ (n\le m < 2(n-2))$ arcs, which is an
analogy to the conjecture for the energy of undirected graphs proposed by
Caporossi {\it et al.} [G. Caporossi, D. Cvetkovi$\acute{c}$, I. Gutman, P.
Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs
with external energy, J. Chem. Inf. Comput. Sci. 39 (1999) 984-996.]
