Based on the first-principles calculations within the density functional theory and crystal structure prediction algorithms iron phosphide phases stable under pressure of the Earth’s core and temperatures up to 4000 K were determined. A new low-temperature modification FeP-P21/c stable above ∼75 GPa was predicted. Fe2P with the allabogdanite structure has been established to be stable in the low-temperature region at ambient conditions. At 750 K it transforms into the barringerite structure. The transition from Fe3P with schreibersite structure to Fe3P-Cmcm was observed at 27 GPa, and the phase transition boundary is nearly isobaric. Fe2P and FeP are thermodynamically stable at the Earth’s inner core pressures and 0 K according to the obtained results, whereas Fe3P stabilizes with respect to decomposition to Fe + Fe2P at high temperatures above ∼3200 K.