  Topological states of matter in non-Hermitian systems have attracted a lot of
attention due to their intriguing dynamical and transport properties. In this
study, we propose a periodically driven non-Hermitian lattice model in
one-dimension, which features rich Floquet topological phases. The topological
phase diagram of the model is derived analytically. Each of its non-Hermitian
Floquet topological phases is characterized by a pair of integer winding
numbers, counting the number of real 0- and \pi-quasienergy edge states at the
boundaries of the lattice. Non-Hermiticity induced Floquet topological phases
with unlimited winding numbers are found, which allow arbitrarily many real 0-
and \pi-quasienergy edge states to appear in the complex quasienergy bulk gaps
in a well-controlled manner. We further suggest to probe the topological
winding numbers of the system by dynamically imaging the stroboscopic spin
textures of its bulk states.
