  Let $ \mathcal{A} $ be a commutative and semisimple Banach algebra with
identity norm one and $ G $ be an abelian locally compact Hausdorff group. In
this paper, we study BSE-Property for $L^1(G,\mathcal A)$ and show that
$L^1(G,\mathcal A)$ is a BSE algebra if and only if $\mathcal A$ is so.
