Ba0.4Sr0.6Ti1−yCoyO3 ceramics show a diphase of Ba1−xSrxTiO3 and 6H-hexagonal BaTi1−yCoyO3. As y increases, Ba0.4Sr0.6Ti1−yCoyO3 ceramics experience a transformation from ferroelectric to relaxor-like behavior. For the samples with y ≥ 0.10, the dielectric constant exhibits relaxor-like behavior with the frequency-dependent temperature of the dielectric peak Tm following an Arrhenius law, accompanying a giant dielectric response. The dielectric relaxation with an extremely high dielectric peak is attributed to charge ordering and defects. The samples with low Co levels (y ≤ 0.05) exhibit dielectric nonlinear behavior, whereas those with high Co levels (y ≥ 0.10) have ferromagnetic properties.