  Using density functional theory based methods we report the structural,
electronic and topological properties of the FCC crystal compound TmBi. This
material is found to be dynamically stable and shows a non magnetic semimetalic
character. By tuning the spin-orbit coupling, we observe a significant change
in the band structure, and the occurrence of band inversion along $\Gamma -X$
direction. The parity product at time-reversal invariant momentum points and
the Wannier charge center calculations provide a topological index $Z_{2}=1$ on
the $k_{j}=0$ plane (with $j=1,2$ and $3$) revealing the non trivial
topological character of TmBi. The existence of topologically protected surface
states of TmBi through the observation of a Dirac cones at $\bar{X}$ point
confirm our finding. The present work could inspire platforms for exploring
novel topological states within the family of rare-earth monobismuthides.
