  In this paper, we introduced the concept of crossed module for Hom-Lie
antialgebras. It is proved that the category of crossed modules for Hom-Lie
antialgebras and the category of $Cat^1$-Hom-Lie antialgebras are equivalent to
each other. The relationship between the crossed module extension of Hom-Lie
antialgebras and the third cohomology group are investigated.
