The effect of pressure on the zone-center optical phonon modes of antimony in the A7 structure has been investigated by Raman spectroscopy. The A(g) and E-g frequencies exhibit a pronounced softening with increasing pressure, the effect being related to a gradual suppression of the Peierls-like distortion of the A7 phase relative to a cubic primitive lattice. Also, both Raman modes broaden significantly under pressure. Spectra taken at low temperature indicate that the broadening is at least partly caused by phonon-phonon interactions. We also report results of ab initio frozen-phonon calculations of the A(g) and E-g mode frequencies. The presence of strong anharmonicity is clearly apparent in calculated total energy versus atom displacement relations. Pronounced nonlinearities in the force versus displacement relations are observed. Structural instabilities of the Sb A7 phase are briefly addressed in the Appendix.