The phonon dispersion relations in a high-density Ne crystal have been measured in the , , and  symmetry directions at 8 K using a triple-axis neutron spectrometer. The crystal was grown at a pressure of 6 kbar and at 82 K in a new high-pressure sample holder. Its lattice parameter was determined to be 4.209 ± 0.002, equivalent to a molar volume which is 84% of that of an equilibrium density crystal at T=0 K. A Born-von Kármán force-constant analysis indicated that the interatomic forces in Ne remain predominantly central in nature at this density. The data are well represented in the harmonic approximation by a Lennard-Jones potential with ε=50.8×10-16 erg and σ=2.818. The force constants from the most general model were used to derive the zero-sound elastic constants. Corrected for pressure, the analysis gives c11=547±8, c12=278±8, and c44=289±4 (108 dyn cm-2). A new analysis of the results of three previous studies of phonon dispersion relations in Ne crystals of approximately equilibrium density was used in conjunction with the present results to derive a dispersion of quasiharmonic mode Grüneisen parameters. These were appropriately summed to obtain the macroscopic Grüneisen parameter. Quasiharmonic calculations were shown to overestimate the compression dependence of the phonon energies in Ne. Further thermodynamic calculations also demonstrated the relative decreased importance of zero-point motion in the high-density crystal.