  A topological superconductor candidate $\beta$-RhPb$_2$ is predicted by using
the first-principles electronic structure calculations. Our calculations show
that there is a band inversion around the Fermi level at the Z point of
Brillouin zone. The calculated nonzero topological invariant Z$_2$ indicates
that $\beta$-RhPb$_2$ is a topological insulator defined on a curved Fermi
level. The slab calculations further demonstrate that the gapless nontrivial
topological surface states (TSS) are not overlapped by the bulk states and they
cross the Fermi level. The phonon calculations confirm the dynamical stability
of $\beta$-RhPb$_2$, while the electron-phonon coupling (EPC) calculations
predict that the superconducting transition temperature ($T_c$) of
$\beta$-RhPb$_2$ can reach 9.7 K. The coexistence of nontrivial topological
band structure with the TSS crossing the Fermi level as well as the
superconducting $T_c$ above the liquid-helium temperature suggest that the
layered compound $\beta$-RhPb$_2$ is a topological superconductor, which
deserves further experimental verification.
