In this paper, we study some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra. In particular, we discuss the relationship between decomposition and completness for a hom-Lie superalgebra. Moreover, we check some conditions that the set of α s -derivations of a hom-Lie superalgebra to be complete and simply complete.

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Complete hom-Lie superalgebras are considered and some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the relation between decomposition and completeness for a hom-Lie superalgebra is described. Moreover, some conditions that the linear space of $$\alpha ^{s}$$ α s -derivations of a hom-Lie superalgebra to be complete and simply complete are obtained.