  In this paper, we propose a first principle calculation method for the
effective Zeeman's coupling based on the second perturbation theory and apply
it to a few topological materials. For Bi and Bi$_2$Se$_3$, our numerical
results are in good accord with the experimental data; for Na$_3$Bi, TaN, and
ZrTe$_5$, the structure of the multi-bands Zeeman's couplings are discussed.
Especially, we discuss the impact of Zeeman's coupling on the Fermi surface's
topology in Na$_3$Bi in detail.
