The phonon dispersion relations in high-density crystals of fcc He4 have been measured along high-symmetry directions by the neutron-inelastic-scattering technique. A recent study of the lattice dynamics of fcc He4 by Eckert et al. has been extended to cover the fcc phase diagram at pressures below 5 kbar. Molar volumes of 9.03, 9.43, and 9.97 cm3/mole have been studied in the temperature range from near the melting curve to near the fcc-hcp transition line. The phonon dispersion relations are in good agreement with a first-order self-consistent phonon theory calculation by Goldman. The observed phonon-group line shapes at large energy and momentum transfers show evidence for multiphonon scattering in agreement with calculations by Glyde. Eckert et al. reported extremely large anharmonic isochoric temperature shifts of the phonon energies. The present work studied the shifts as a function of molar volume and temperature. Mode-Grüneisen-parameter dispersion curves have been measured using the present data and earlier measurements at lower density in the fcc phase by Traylor et al. Macroscopic Grüneisen parameters have been calculated from the phonon density of states obtained from the data.