  Let $L_{D_8}(1, 0)$ and $L_{E_8}(1, 0)$ be the simple vertex operator
algebras associated to untwisted affine Lie algebra $\widehat{{\mathbf
g}}_{D_{8}}$ and $\widehat{{\mathbf g}}_{E_8}$ with level 1 respectively. In
the 1980s by I. Frenkel, Lepowsky and Meurman as one of the many important
preliminary steps toward their construction of the moonshine module vertex
operator algebra, they use roots lattice showing that $L_{D_8}(1, 0)$ can embed
into $L_{E_8}(1, 0)$ as a vertex operator subalgebra(\cite{5, 6, 8}). Their
construct is a base of vertex operator theory.
  But the embedding they gave using the fact $L_{\mathbf g}(1,0)$ is isomorphic
to its root lattice vertex operator algebra $V_L$. In this paper, we give an
explicitly construction of the embedding and show that as an $L_{D_8}(1,
0)$-module, $L_{E_8}(1, 0)$ is isomorphic to the extension of $L_{D_8}(1, 0)$
by its simple module $L_{D_8}(1, \overline{\omega}_8)$. It may be convenient to
be used for conformal field theory.
