The discovery of new high-temperature superconductors based on FeAs has led to a new ‘gold rush’ in high-T_C superconductivity. All of the new superconductors share the same common structural motif of FeAs layers and reach T_C values up to 55 K (ref. ). Recently, superconductivity has been reported in FeSe (ref. ), which has the same iron pnictide layer structure, but without separating layers. Here, we report the magnetic and electronic phase diagram of β-Fe_1.01Se as a function of temperature and pressure. The superconducting transition temperature increases from 8.5 to 36.7 K under an applied pressure of 8.9 GPa. It then decreases at higher pressures. A marked change in volume is observed at the same time as T_C rises, owing to a collapse of the separation between the Fe₂Se₂ layers. No static magnetic ordering is observed for the whole p–T phase diagram. We also report that at higher pressures (starting around 7 GPa and completed at 38 GPa), Fe_1.01Se transforms to a hexagonal NiAs-type structure and exhibits non-magnetic behaviour.