Raman spectra of isotopically pure zinc-blende CuBr ((CuBr)-Cu-63-Br-81) were measured at T = 10 K un der hydrostatic pressures up to 4 GPa. The ambient-pressure spectrum consists of a transverseoptic (TO) phonon line and an anomalous broad band located at frequencies near the expected first-order longitudinal-optic (LO) scattering. Application of hydrostatic pressure leads to an increase of the linewidth uf the TO mode and to a significant change of the LO scattering band which above 3 GPa develops into a single LO phonon peak of narrow linewidth. The disappearance of the LO Raman anomaly as well as the broadening of the TO mode with pressure are explained by pressure-dependent third-order anharmonic interactions of zone-center optical phonons with q = 0 two-phonon states.