A high-throughput screening using density functional calculations is performed to search for stable boride superconductors from the existing materials database. The workflow employs the fast frozen phonon method as the descriptor to evaluate the superconducting properties quickly. 23 stable candidates are identified from the screening. For almost all found binary compounds, the superconductivity was obtained earlier experimentally or computationally. For ternary borides, previous studies are very limited. Our extensive search among ternary systems confirmed superconductivity in known systems and found several new compounds. Among these discovered superconducting ternary borides, Ta(MoB)$_2$ shows the highest superconducting temperature of ~12K. Most predicted compounds were synthesized previously; therefore, our predictions can be examined experimentally. Our work also demonstrates that the boride systems can have diverse structural motifs that lead to superconductivity.