In this talk we will discuss a canonical asymptotic expansion up to infinite order of the K\"{a}hler-Einstein metric on a compact complex manifold complement of a simple normal crossings divisor. This work is parallel to the asymptotics of Fefferman, Lee and Melrose on the strictly pseudoconvex domain in $\bf{C}^n$. At the end we will mention some possible applications related to complex geometry and algebraic geometry