Let $G$ be a graph of order $n$. The energy $\mathcal{E}(G)$ of a simple graph $G$ is the sum of absolute values of the eigenvalues of its adjacency matrix. The Laplacian energy, the signless Laplacian energy and the distance energy of graph $G$ are denoted by $LE(G)$, $SLE(G)$ and $DE(G)$, respectively. In this paper we introduce a distance Laplacian energy $DLE$ and distance signless Laplacian energy $DSLE$ of a connected graph. We present Nordhaus-Gaddum type bounds on Laplacian energy $LE(G)$ and signless Laplacian energy $SLE(G)$ in terms of order $n$ of graph $G$ and characterize graphs for which these bounds are best possible. The complete graph and the star give the smallest distance signless Laplacian energy $DSLE$ among all the graphs and trees of order $n$, respectively. We give lower bounds on distance Laplacian energy $DLE$ in terms of $n$ for graphs and trees, and characterize the extremal graphs. Also we obtain some relations between $DE$, $DSLE$ and $DLE$ of graph $G$. Moreover, we give several open problems in this paper.