The mechanism of superconductivity in cuprates remains one of the big challenges of condensed matter physics. High-Tc cuprates crystallize into a layered perovskite structure featuring copper oxygen octahedral coordination. Due to the Jahn Teller effect in combination with the strong static Coulomb interaction, the octahedra in high-Tc cuprates are elongated along the c axis, leading to a 3dx²-y² orbital at the top of the band structure wherein the doped holes reside. This scenario gives rise to 2D characteristics in high-Tc cuprates that favor d-wave pairing symmetry. Here, we report superconductivity in a cuprate Ba₂CuO4-y, wherein the local octahedron is in a very exceptional compressed version. The Ba₂CuO4-y compound was synthesized at high pressure at high temperatures and shows bulk superconductivity with critical temperature (Tc ) above 70 K at ambient conditions. This superconducting transition temperature is more than 30 K higher than the Tc for the isostructural counterparts based on classical La₂CuO₄. X-ray absorption measurements indicate the heavily doped nature of the Ba₂CuO4-y superconductor. In compressed octahedron, the 3d3z²-r² orbital will be lifted above the 3dx²-y² orbital, leading to significant 3D nature in addition to the conventional 3dx²-y² orbital. This work sheds important light on advancing our comprehensive understanding of the superconducting mechanism of high Tc in cuprate materials.