  For virtual knot theory, the virtual braid group was defined by generalizing
the braid group. It was proved that any virtual link can be obtained by the
closure of a virtual braid. On the other hand, due to work by Jones et al., it
is known that any (oriented) link is constructed from an element of Thompson's
group $F$. In this paper, we define the ``virtual version'' of Thompson's group
$F$ and prove that any virtual link is constructed from an element of the
group.
