Ternary hydrides are considered as promising materials for high temperature (Tc) superconductors under high pressure due to the expansion of congratulational space compared to binary hydrides. Here, by using a swarm intelligence structure search method combined with density functional theory, we investigate the crystal structures, the electronic properties and the superconductivity of Ce-B-H systems at 100 GPa and 200 GPa. We identified six thermal dynamically stable Ce-B-H compounds, namely CeBH, CeBH6, CeBH7, Ce2BH14, Ce2BH16 and CeB2H3. All of them exhibit metallic nature. Among these, CeBH6, Ce2BH14, and Ce2BH16 are predicted to be superconducting, and Ce2BH14 exhibit the maximum Tc of 64 K at 100 GPa. The analysis reveals that the coupling between f electron from metal Ce and phonons derived from B and H at mid-frequencies plays a key role in the superconductivity. Our results could be used to guide future experimental synthesis of new ternary hydrides with the aid of high pressure.