We have fabricated (Ba,Sr)TiO3$TiO_3$ thick films doped with various amount of ZnBO dopants (1, 3, and 5 wt%) by screen printing method on the alumina substrates, which were sintered at the temperature below $1200^{circ}C$. With increasing the amount of ZnBO dopants, the relative dielectric permittivity of ZnBO doped (Ba,Sr)$TiO_3$ was decreased, while loss tangent was increased. 1 wt% ZnBO doped (Ba,Sr)$TiO_3$ thick film has relative dielectric permittivity of 759 at 1 MHz, while 3 and 5 wt% of ZnBO doped (Ba,Sr)$TiO_3$ thick films have 624 and 554, respectively. By introducing ZnBO dopants to the (Ba,Sr)$TiO_3$ thick films, leakage current densities were decreased. The decreased leakage current with increasing ZnBO dopants can be explained by increased density and grain size of thick film on alumina substrate. We believe this decreased leakage current density probably come from the increased grain size and increased density.