  In this work we deal with coverings and actions of Lie group- groupoids being
a sort of the structured Lie groupoids. Firstly, we define an action of a Lie
group-groupoid on some Lie group and the smooth coverings of Lie
group-groupoids. Later, we show the equivalence of the category of smooth
actions of Lie group-groupoids on Lie groups and the category of smooth cov-
erings of Lie group-groupoids. Further, we prove a theorem which denotes how is
obtained a covering Lie group-groupoid and a smooth covering morphism of Lie
group-groupoids from a Lie group-groupoid.
