  For a simple digraph $G$ of order $n$ with vertex set $\{v_1,v_2,\ldots,
v_n\}$, let $d_i^+$ and $d_i^-$ denote the out-degree and in-degree of a vertex
$v_i$ in $G$, respectively. Let $D^+(G)=diag(d_1^+,d_2^+,\ldots,d_n^+)$ and
$D^-(G)=diag(d_1^-,d_2^-,\ldots,d_n^-)$. In this paper we introduce
$\widetilde{SL}(G)=\widetilde{D}(G)-S(G)$ to be a new kind of skew Laplacian
matrix of $G$, where $\widetilde{D}(G)=D^+(G)-D^-(G)$ and $S(G)$ is the
skew-adjacency matrix of $G$, and from which we define the skew Laplacian
energy $SLE(G)$ of $G$ as the sum of the norms of all the eigenvalues of
$\widetilde{SL}(G)$. Some lower and upper bounds of the new skew Laplacian
energy are derived and the digraphs attaining these bounds are also determined.
