The low-enthalpy structures of Th-B-H ternary compounds below 50 GPa are investigated by using an efficient framework that combines high-throughput screening, genetic algorithms, and first-principles calculations. Four thermodynamically stable hydrides (Th2BH11, Th2BH10, ThB2H10, and ThBH) and seven thermodynamically metastable hydrides (ThBH2, ThBH3, ThBH4, ThBH5, ThBH7, ThB2H4, and ThB3H3) are revealed. There are no stable thorium boron hydrides at ambient pressure. R3m-ThB2H10 and R3m-Th2BH11 are indirect bandgap semiconductors, while R3m-Th2BH10 and P6/mmm-ThBH show metallic nature. The relatively low λ values of R3m-Th2BH10 and P6/mmm-ThBH result in their Tc around 5.8 K and 0.1 K at 20 GPa, respectively. Two metastable phases, F4¯3m-ThBH5 and P63/mmc-ThBH7, exhibit excellent superconducting properties at low pressures. The values of Tc of F4¯3m-ThBH5 and P63/mmc-ThBH7 reach 46.9 K at 20 GPa and 40.0 K at 50 GPa, respectively. Our findings offer valuable insights for discovering and designing superconducting rare earth hydrides under low and even ambient pressures.