In the atmosphere of $N_2$ gas, BaZ $r_{0.08}$ $Ti_{0.92}$ $O_3$ polycrystal was grown by floating zone technique using BaZ $r_{0.08}$ $Ti_{0.92}$ $O_3$ ceramics as a feed and SrTi $O_3$(1l0) single cystal as a seed. The dielectric constant and loss at 10 kHz, 100 kHz, and 1 MHz for the as-grown sample were measured as a function of temperature in the temperature range between -10$0^{circ}C$ and 150 $^{circ}C$ to find a dielectric peak with frequency dispersion at Curie point. The hysteresis loop showed that the grown sample had very small polarization which was 0-0.01 $mu$C/$ extrm{cm}^2$ for the applied dc-electric fields from -7 kV/cm to +7 kV/cm. However, the normal hysteresis loop was appeared after oxygen annealing. The electric-field dependence of the dielectric constant for both the as-grown and the post-annealed samples was studied by measuring the dielectric constants as a function of the biased-electric fields and their tunability was figured out from it at room temperature(27 $^{circ}C$) and cryotemperature( -73$^{circ}C$). Tunability for the as-grown sample was 51 % and the figure of merit 20.4 at 10kHz with the biased electric-field of 12 kV/cm. The tunability for the grown sample may be increased up to 80 % if the electric field of 25 kV/cm is applied. Tunability for the post-annealed sample was 41 % and the figure of merit 10.3 at 10 kHz with the biased electric-field of 12 kV /cm. Post-annealing improved the crystallinity of the as-grown sample but decreased its tunability.ability.