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. 2). Recently, superconductivity has been reported in FeSe (ref. 3), which has the same iron pnictide layer structure, but without separating layers. Here, we report the magnetic and electronic phase diagram of beta-Fe(1.01)Se 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 Fe(2)Se(2) 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(1.01)Se transforms to a hexagonal NiAs-type structure and exhibits non-magnetic behaviour.