  We study the topological properties of Peierls transitions in a monovalent
M\"{o}bius ladder. Along the transverse and longitudinal directions of the
ladder, there exist plenty Peierls phases corresponding to various dimerization
patterns. Resulted from a special modulation, namely, staggered modulation
along the longitudinal direction, the ladder system in the insulator phase
behaves as a ``topological insulator'', which possesses charged solitons as the
gapless edge states existing in the gap. Such solitary states promise the
dispersionless propagation along the longitudinal direction of the ladder
system. Intrinsically, these non-trivial edges states originates from the
Peierls phases boundary, which arises from the non-trivial $\mathbb{Z}^{2}$
topological configuration.
