A new TeZnO3 phase was synthesized by high-pressure techniques. Different from the ambient-pressure orthorhombic phase composed of ZnO5 units, the current high-pressure one crystallizes to a monoclinic structure with space group P2(1)/n. Moreover, both ZnO4 tetrahedral and ZnO6 octahedral polyhedra are found to occur in this new phase, providing a unique Zn-based material system that simultaneously possesses two distinct coordinated units. Because the outermost orbitals are fully occupied for both Zn2+ and Te4+, the compound exhibits diamagnetism and strong insulating behavior with a wide bandgap as large as 6.0 eV. Dielectric constant and specific heat measurements show a broad anomaly around 240 K Low-temperature synchrotron X-ray diffraction reveals an isostructural phase transition at this temperature.