BaAl(2-2x)(Zn0.5Si0.5)2xO4 (x = 0, 0.2, 0.4, 0.6, 0.8, 1.0) solid solutions with weak ferroelectricity were prepared using a conventional solid-state reaction method. Zn atoms preferentially occupied the 6c-Wyckoff site of Al1 and the 2b-Wyckoff site of Al4, whereas Si atoms filled the 6c-Wyckoff site of Al2 and the 2b-Wyckoff site of Al3. As such, the cell volume shrank abnormally as the number of larger [Zn0.5Si0.5]3+ compared to Al3+ increased. There were two anomalous peaks in the dielectric constant. One peak at low temperature represented a second-order ferroelectric transition. Relaxor-like behaviour and a stable dielectric constant against temperature from -50 °C to 400 °C were observed at x = 0.4. This result was attributed to disorder in the 2b-Wyckoff site Al/(Zn0.5Si0.5) and distortion in the tetrahedron.