  In this paper we investigate some important basic properties of simple
Hom-Lie superalgebras and show that a Hom-Lie superalgebra does not have any
left or right nontrivial ideals. Moreover, we classify invariant bilinear forms
on a given simple Hom-Lie superalgebra. Then we study the Killing forms on a
Hom-Lie algebra which are examples of the invariant bilinear forms. Making use
of the Killing forms, we find conditions for a Hom-Lie superalgebra to be
classical. Furthermore, we check the conditions in which the Killing form of a
Hom-Lie superalgebra is non-degenerate.
