  By means of first-principles and \emph{ab initio} tight-binding calculations,
we found that the compound of NaBi is a three-dimensional non-trivial
topological metal. Its topological feature can be confirmed by the presence of
band inversion, the derived effective Z$_2$ invariant and the non-trivial
surface states with the presence of Dirac cones. Interestingly, our
calculations further demonstrated that NaBi exhibits the uniquely combined
properties between the electron-phonon coupling superconductivity in nice
agreement with recent experimental measurements and the obviously anisotropic
but extremely low thermal conductivity. The spin-orbit coupling effects greatly
affect those properties. NaBi may provide a rich platform to study the
relationship among metal, topology, superconductivity and thermal conductivity.
