The mechanism of superconductivity in cuprates remains one of the big challenges of condensed matter physics.High Tc cuprates crystallize into 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 two dimensional 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 three dimensional nature in addition to the conventional 3dx2-y2 orbital. This work sheds important new light on advancing our comprehensive understanding of the superconducting mechanism of high Tc in cuprate materials.