  In this note we give a new upper bound for the Laplacian eigenvalues of an
unweighted graph. Let $G$ be a simple graph on $n$ vertices. Let $d_{m}(G)$ and
$\lambda_{m+1}(G)$ be the $m$-th smallest degree of $G$ and the $m+1$-th
smallest Laplacian eigenvalue of $G$ respectively. Then $ \lambda_{m+1}(G)\leq
d_{m}(G)+m-1 $ for $\bar{G} \neq K_{m}+(n-m)K_1 $. We also introduce upper and
lower bound for the Laplacian eigenvalues of weighted graphs, and compare it
with the special case of unweighted graphs.
