Fe–P binary compounds have attracted much attention, particularly under high pressure, since they are the constituents of the Earth's core. However, most studies focus on the single stoichiometry of Fe–P binary compounds at high pressure, and their whole phase diagram and relative stabilities have been unexplored thus far. Herein, first principles swarm structure predictions are performed to find stable structures of Fe–P compounds with various Fe_xP_y (x = 1–4 and y = 1, or x = 1 and y = 2) compositions. Then, their phase diagram and relative stabilities are reliably determined based on predicted structures. Specifically, the FeP, Fe₂P and Fe₄P compounds are found to be stable in the pressure range of 0–400 GPa. The Fe₃P compound decomposes into Fe₂P and Fe₄P above 214 GPa. FeP₂ becomes unstable above 82 GPa. Notably, two new phases (i.e. C2/c-structured Fe₄P and Cmcm-structured Fe₃P) are found to be more stable than the previously reported phases. In addition, the XRD pattern of the predicted Cmcm-structured Fe₃P matches the experimental patterns, and we are awaiting future experimental confirmation. Electronic band calculations show that the Fe–P binary compounds are metallic, with a pronounced Fe 3d component crossing the Fermi level. Cmcm-structured Fe₃P is ferromagnetic. Our study not only provides useful information for the further study of Fe–P binary compounds but also for the determination of the Earth's core components.