  Let $X$ be a metrizable space and ${\rm Comp}(X)$ be the hyperspace
consisting of non-empty compact subsets of $X$ endowed with the Vietoris
topology. In this paper, we give a necessary and sufficient condition on $X$
for ${\rm Comp}(X)$ to be homeomorphic to a non-separable Hilbert space.
Moreover, we consider the topological structure of pair $({\rm
Comp}(\overline{X}),{\rm Fin}(X))$ of hyperspaces of $X$ and its completion
$\overline{X}$, where ${\rm Fin}(X)$ is the hyperspace of non-empty finite sets
in $X$.
