We examine the ferroelectric-relaxor behavior of (Ba0.65Sr0.35)(Zr0.35Ti0.65)O3 (BSZT) ceramics in the temperature range from 80 to 380 K. A broad dielectric maximum, which shifts to higher temperature with increasing frequency, signifies the relaxor-type behavior of these ceramics. The value of the relaxation parameter γ∼2 estimated from the linear fit of the modified Curie–Weiss law, indicates the relaxor nature of the BSZT ceramics. The dielectric relaxation rate follows the Vogel–Fulcher relation with TVF=107 K, Ea=0.121 eV, and ν0=6.83×1014 Hz, further supports such relaxor nature. The slim P–E hysteresis loop and ‘butterfly’ shape dc bias field dependence of permittivity at T>Tm (Tm, the temperature of permittivity maximum) clearly signifies the occurrence of nanopolar clusters, which is the typical characteristic of ferroelectric relaxor. At 300 K and 10 kHz, the dielectric constant and loss tan δ are ∼1100 and 0.0015, respectively. The high tunability (∼25%) and figure of merit (∼130) at room temperature show that the BSZT ceramics could be a promising candidate for tunable capacitor applications.