Inelastic neutron scattering measurements were performed with a time-of-flight chopper spectrometer to observe phonons in all parts of the Brillouin zone of a single crystal of cuprite Cu2O. We reduced the experimental data to phonon dispersions in the high-symmetry directions, and changes between 10 and 300 K are reported. In this paper, we show ab initio quasiharmonic (QH) and anharmonic (AH) calculations of phonon dispersions. We performed all AH calculations with a temperature-dependent effective potential method. Both QH and AH calculations account for the small negative thermal expansion of cuprite at low temperatures. However, the measured temperature-dependent phonon behavior was predicted more accurately with the AH calculations than the QH ones. Nevertheless, at 300 K, the cubic AH used in this paper did not entirely account for the experimental phonon dispersions in cuprite.