  A distinct electronic structure was observed in the single-layer FeSe which
shows surprising high temperature superconductivity over 65k. Here we
demonstrate that the electronic structure can be explained by the strain effect
due to substrates. More importantly, we find that this electronic structure can
be tuned into robust topological phases from a topologically trivial metallic
phase by the spin-orbital interaction and couplings to substrates. The
topological phase is robust against any perturbations that preserve the
time-reversal symmetry. Our studies suggest that topological phases and
topologically related properties such as Majorana Fermions can be realized in
iron-based high T$_{c}$ superconductors.
