We measured phonon dispersions of CaFe₂As₂ using inelastic neutron scattering and compared our results to predictions of density functional theory in the local density approximation. The calculation gives correct frequencies of most phonons if the experimental crystal structure is used, except observed linewidths/frequencies of certain modes were larger/softer than predicted. Strong temperature dependence
of some phonons near the structural phase transition near 172 K may indicate strong electron-phonon coupling and/or anharmonicity, which may be important for superconductivity.