The structural and electronic properties of BiCoO3 under high pressure have been investigated. Synchrotron X-ray and neutron powder diffraction studies show that the structure changes from a polar PbTiO3 type to a centrosymmetric GdFeO3 type above 3 GPa with a large volume decrease of 13% at room temperature revealing a spin-state change. The first-order transition is accompanied by a drop of electrical resistivity. Structural results show that Co3+ is present in the low spin state at high pressures, but X-ray emission spectra suggest that the intermediate spin state is present. The pressure−temperature phase diagram of BiCoO3 has been constructed enabling the transition temperature at ambient pressure to be estimated as 800−900 K.