The elastic properties of unpoled and prepoled (Na1/2Bi1/2)TiO3-xBaTiO3 (NBT-xBT) single crystals near the morphotropic phase boundary were investigated as a function of temperature using Brillouin light scattering. The acoustic mode frequency and the related acoustic damping of unpoled NBT-xBT showed very broad minimum and maximum, respectively, consistent with typical relaxor behaviors. The frequency softening of the longitudinal acoustic mode together with the increase in acoustic damping was largest along the <100> direction, indicating that polarization fluctuations were most substantial along this crystallographic direction. The difference in acoustic behaviors between the unpoled NBT-xBTs with x = 0.05 and 0.08 were negligible, which means that the NBT-xBT system exhibits typical relaxor properties over a certain composition range of at least 5~8%. The obtained relaxation time of polar nanoregions in the paraelectric phase showed a gradual slowing-down character without any critical divergent behavior. The prepoling of NBT-xBT along the <100> direction induced drastic changes in both mode frequency and damping at ~110 °C when the poling field was larger than 1.4 kV/mm, corresponding to the depoling process from macroscopic/mesoscopic ferroelectric order to ergodic relaxor state upon heating. Phase coexistence of ferroelectric and relaxor states was observed at the intermediate poling field of 1.4 kV/mm.