  Let $G$ be a graph with maximum degree $\Delta$, and let $G^{\sigma}$ be an
oriented graph of $G$ with skew adjacency matrix $S(G^{\sigma})$. The skew
spectral radius $\rho_s(G^{\sigma})$ of $G^\sigma$ is defined as the spectral
radius of $S(G^\sigma)$. The skew spectral radius has been studied, but only
few results about its lower bound are known. This paper determines some lower
bounds of the skew spectral radius, and then studies the oriented graphs whose
skew spectral radii attain the lower bound $\sqrt{\Delta}$. Moreover, we apply
the skew spectral radius to the skew energy of oriented graphs, which is
defined as the sum of the norms of all the eigenvalues of $S(G^\sigma)$, and
denoted by $\mathcal{E}_s(G^\sigma)$. As results, we obtain some lower bounds
of the skew energy, which improve the known lower bound obtained by Adiga et
al.
