Hollandite-type Ba_1−xSr_xZnTi₇O₁₆ (x=0, 0.2, 0.4, 0.6, 0.8, and 1) ceramics have been synthesized by the conventional solid-state ceramic route. The phase purity and microstructure of these compositions have been characterized using x-ray diffraction (XRD) and scanning electron microscopy (SEM). The XRD analysis shows that an increase in strontium concentration in the A-site causes pairing of vacant tunnel sites, and hence the structure becomes unstable due to the collapse of the tunnel walls. The dielectric properties such as dielectric constant (ε_r), loss tangent (tan δ), and temperature variation of dielectric constant (τε_r) have been measured up to the 13 MHz region. The present study shows that zinc hollandites have relatively high dielectric constant and low loss tangent. The temperature variation of dielectric constant studies reveal that Ba-rich compositions have high positive τε_r and Sr-rich compositions have high negative τε_r in the 0–100°C region. Proper tailor making of these compositions has been attempted to arrive at near-zero temperature variation of the dielectric constant.