  The aim of this paper is to define the notion of lifting of a crossed module
via a group morphism and give some properties of this type of the lifting.
Further we obtain a criterion for a crossed module to have a lifting of crossed
module. We also prove that the liftings of a certain crossed module constitute
a category; and that this category is equivalent to the category of covers of
that crossed module and hence to the category of group-groupoid actions of the
corresponding groupoid to that crossed module.
