\input zb-basic \input zb-ioport \iteman{io-port 05850465} \itemau{Liu, Ying; Sun, Yu Qin} \itemti{On the second Laplacian spectral moment of a graph.} \itemso{Czech. Math. J. 60, No. 2, 401-410 (2010).} \itemab Summary: {\it M. Lazi\'{c}} [Czech. Math. J. 56, No.~4, 1207--1213 (2006; Zbl 1164.05408)]) gave the definition of Laplacian energy of a graph $G$ and proved $\operatorname{LE}(G)\geq 6n-8$, where equality holds if and only if $G=P_n$. In this paper, we consider the relation between the Laplacian energy and the chromatic number of a graph $G$ and give an upper bound for the Laplacian energy on a connected graph. \itemrv{~} \itemcc{} \itemut{Laplacian eigenvalue; Laplacian energy; chromatic number; complement} \itemli{doi:10.1007/s10587-010-0043-1} \end