Sr2IrO4 with strong spin-orbit coupling and Hubbard repulsion (U) hosts Mott insulating states. The similar crystal structure and magnetic and electronic properties, particularly the d-wave gap observed in Sr2IrO4 enhanced the analogies to the cuprate high-Tc superconductor, La2CuO4. The incomplete analogy was due to the lack of broken inversion symmetry phases observed in Sr2IrO4. Here, under high-pressure and high-temperature conditions, we report a noncentrosymmetric Sr2IrO4. The crystal structure and its noncentrosymmetric character were determined by single-crystal X-ray diffraction and high-resolution scanning transmission electron microscopy. The magnetic characterization confirms the Ir4+ with S = 1/2 at low temperature in Sr2IrO4 with magnetic ordering occurring at around 86 K, where a larger moment is observed than the ambient pressure Sr2IrO4. Moreover, the resistivity measurement shows three-dimensional Mott variable-range hopping (VRH) existed in the system. This noncentrosymmetric Sr2IrO4 phase appears to be a unique material that offers a further understanding of high-Tc superconductivity.