  Given a graph $G$, denote by $\Delta$ and $\chi^\prime$ the maximum degree
and the chromatic index of $G$, respectively. A simple graph $G$ is called {\it
edge-$\Delta$-critical} if $\chi^\prime(G)=\Delta+1$ and
$\chi^\prime(H)\le\Delta$ for every proper subgraph $H$ of $G$. We proved that
every edge chromatic critical graph of order $n$ with maximum degree at least
$\frac{2n}{3}+12$ is Hamiltonian.
