The dielectric spectroscopy of perovskite Ba(Ti0.675Zr0.325)O3 (BTZ325) relaxor ceramics is performed in a wide frequency range of 10−2–106 Hz. In contrast to other known relaxors, where the dipole dynamics is subject to non-Arrhenius slowing-down and freezing upon cooling so that the cubic ergodic relaxor phase transforms into a cluster dipolar-glass phase or a ferroelectric phase, none of these transformations are observed in BTZ325. In the course of cooling from the ergodic relaxor phase the characteristic time and the spectral width of the main relaxation process first increase rapidly in a Vogel–Fulcher manner, but then become almost temperature independent below the temperature of permittivity maximum, indicating the onset of the state which we call quasi-ferroelectric. The properties and the origin of this state are discussed.