  We construct a two-leg ladder dimer model by using two orbitals instead of
one in Su-Schrieffer-Heeger (SSH) dimer chain and find out a chiral symmetry in
it. In this model, the otherwise-hidden additional chiral symmetry allows us to
define two chiral massless fermions and show that there exist interesting
topological states characterized by $\mathbb{Z}\oplus\mathbb{Z}$ and
corresponding zero mode edge states. Our complete phase diagram reveals that
there is an anomalous topologically nontrivial region in addition to the normal
one similar to that of SSH model. The anomalous region features that the
inter-cell hopping constants can be much smaller than the intra-cell ones,
being opposite to the normal region, and the zero mode edge states do not have
well-defined parity each. Finally, we suggest that this ladder dimer model can
be realized in double-well optical lattices, ladder polymer systems, and adatom
double chains on semiconductor surfaces.
