In this paper, we define a new type of cohomology for Hom-Leibniz superalgebras which controls deformations of Hom-Leibniz superalgebras. The cohomology and the associated deformation theory for Hom-Leibniz superalgebras as developed here are also extended to equivariant context, under the presence of finite group actions on Hom-Leibniz superalgebras.