Central peaks and acoustic phonons of 0.91Pb(Zn1/3Nb2/3)-0.09PbTiO3 (0.91PZN-0.09PT) relaxor single crystals have been studied in detail by a micro-Brillouin scattering technique. Two phase transitions from cubic to tetragonal and tetragonal to rhombohedral upon cooling are observed through the frequency shifts and damping of the acoustic phonons. 0.91PZN-0.09PT near morphotropic phase boundary is heterogeneous, and the heterogeneity is studied by scanning the incident laser spot over the crystal sample. Elastic constant c33 and sound velocity vLA are determined. Central peaks have been directly observed, they show marked temperature dependence both in intensity and width; they are closely related to the fluctuations of polar microregions. Relaxation times are obtained and the mechanisms of central peaks are discussed.