Materials that exhibit both superconductivity and nontrivial topological electronic structures have attracted considerable attention due to the potential for the realization of novel quantum states. Here, using swarm-intelligence structure prediction methodology and first-principles calculations, we have predicted a ternary double-metal boron clathrate superconductor LiLaB8 with topologically protected surface states. B atoms in LiLaB8 polymerize into two kinds of caged structures, i.e. B12 and B24 cages, enclosing Li and La atoms, respectively. LiLaB8 can be possibly synthesized at the pressure above 75 GPa and recovered to ambient conditions with B cages well preserved. Electron-phonon coupling calculations show that LiLaB8 is a potential superconductor with an estimated Tc of 2.4 K at 100 GPa, which increases to 9.5 K at ambient pressure. The enhanced superconductivity is considered to originate from softened mode related to the vibrations of La and B atoms. Electronic band structure calculations showcase the apparent “band inversion” of La 5d and B 2p orbitals. Z2 invariant and topologically protected surface states demonstrate that LiLaB8 is indeed a nontrivial-topological material. These results indicate LiLaB8 is a superconductor with nontrivial band topology that helps in the study of fascinating phenomena arising from the interplay of and superconductivity and band topology.