GeTe/Sb2Te3 superlattice phase-change memory devices demonstrated greatly improved performance over that of Ge2Sb2Te5, a prototype record media for phase-change random access memory. In this work, we show that this type of GeTe/Sb2Te3 superlattice exhibits topological insulating behavior on the basis of ab initio calculations. The analysis of the band structures and parities as well as Z2 topological invariants unravels the topological insulating nature in these artificial materials. Furthermore, the topological insulating character remains in the GeTe/Sb2Te3 superlattice under small compressive strains, whereas it is not observed as more Sb2Te3 building blocks introduced in the superlattice. The present results show that multifunctional data storages may be achieved in the GeTe/Sb2Te3 superlattice. Such kinds of artificial materials can be used in phase-change random access memory, spintronics, and quantum computing.