We present a comprehensive investigation of lattice dynamics in the double-helix antiferromagnet FeP by means of high-resolution time-of-flight neutron spectroscopy and ab initio calculations. Phonons can hybridize with the magnetic excitations in noncollinear magnets to significantly influence their properties. We observed a rich spectrum of phonon excitations, which extends up to similar to 50 meV. We performed detailed analysis of the observed and calculated spectra for all high-symmetry points and high-symmetry directions of the Brillouin zone. We show that the DFT calculations quantitatively capture the essential features of the observed phonons, including both dispersions and scattering intensities. By making use of the detailed intensity comparison between the theory and the data, we were able to identify displacement vectors for the majority of the observed modes. The overall excellent agreement between the DFT predictions and the experimental results breaks down for the lowest mode at the Y point, whose energy is lower than calculated by similar to 13%. The present study provides vital information on the lattice dynamics in FeP and demonstrates applicability of the DFT to novel pressure-induced phenomena in related materials, such as MnP and CrAs.