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Indium antimonide (InSb) nanowires are used as building blocks for quantum devices because of their unique properties, that is, strong spin-orbit interaction and large Landé g-factor. Integrating InSb nanowires with other materials could potentially unfold novel devices with distinctive functionality. A prominent example is the combination of InSb nanowires with superconductors for the emerging topological particles research. Here, the combination of the II–VI cadmium telluride (CdTe) with the III–V InSb in the form of core–shell (InSb–CdTe) nanowires is investigated and potential applications based on the electronic structure of the InSb–CdTe interface and the epitaxy of CdTe on the InSb nanowires are explored. The electronic structure of the InSb–CdTe interface using density functional theory is determined and a type-I band alignment is extracted with a small conduction band offset ( ⩽0.3 eV). These results indicate the potential application of these shells for surface passivation or as tunnel barriers in combination with superconductors. In terms of structural quality, it is demonstrated that the lattice-matched CdTe can be grown epitaxially on the InSb nanowires without interfacial strain or defects. These shells do not introduce disorder to the InSb nanowires as indicated by the comparable field-effect mobility measured for both uncapped and CdTe-capped nanowires.