  We study theoretically the interplay effect of Zeeman field and modulated
spin-orbit coupling on topological properties of a one-dimensional dimerized
lattice, known as Su-Schrieffer-Heeger model. We find that in the weak (strong)
modulated spin-orbit coupling regime, trivial regions or nontrivial ones with
two pairs of zero-energy states can be turned into nontrivial regions by
applying a uniform (staggered) perpendicular Zeeman field through a topological
phase transition. Furthermore, the resulting nontrivial phase hosting a pair of
zero-energy boundary states can survive within a certain range of the
perpendicular Zeeman field magnitude. Due to the effective time-reversal,
particle-hole, chiral, and inversion symmetries, in the presence of either
uniform or staggered perpendicular Zeeman field, the topological class of the
system is BDI which can be characterized by $\mathbbm{Z}$ index. We also
examine the robustness of the nontrivial phase by breaking the underlying
symmetries giving rise that inversion symmetry plays an important role.
