Epitaxial growth, as a best strategy to attain a heterostructure with a well-defined and clean interface, usually takes place on a planar substrate. In this paper, using a ZnO/SnO2 core-shell heterostructure as an example, we demonstrate the possibility of establishing a three-dimensional epitaxial interface between two materials with different crystal systems for the first time and show possible tailoring optical properties by building the heteroepitaxial crystal interface. The characterization results of element mapping, high-resolution transmission electron microscopy, and selected area electric diffraction reveal that the as-prepared ZnO/SnO2 heterostructure has a tetrapod-like ZnO core and a SnO2 shell with 15-30 nm, and their special epitaxial relation is (010)SnO2//(010)ZnO and [100]SnO2//[0001]ZnO. Such three-dimensional epitaxy between the ZnO core and SnO2 shell is quite different from the usual planar epitaxy or three-dimensional epitaxy between materials having the same crystal structure. A rational model of such complicated epitaxy has been proposed through investigating the certain structural comparability between the wurtzite ZnO and rutile SnO2 crystals. The as-prepared T-ZnO/SnO2 epitaxial heterostructure exhibits unique luminescence properties in contrast with individual tetrapod ZnO and SnO2 nanostructures, in which the epitaxial interface induces new luminescence properties. This result may inspire great interest in exploring other complicated epitaxy systems and their potential applications in laser, gas sensor, solar energy conversion, photo catalysis, and nanodevices in the future.