  Bulk-boundary correspondence, connecting the bulk topology and the edge
states, is an essential principle of the topological phases. However, the
bulk-boundary correspondence is broken down in general non-Hermitian systems.
In this paper, we construct one-dimensional non-Hermitian Su-Schrieffer-Heeger
model with periodic driving that exhibits non-Hermitian skin effect: all the
eigenstates are localized at the boundary of the systems, whether the bulk
states or the zero and the $\pi$ modes. To capture the topological properties,
the non-Bloch winding numbers are defined by the non-Bloch periodized evolution
operators based on the generalized Brillouin zone. Furthermore, the
non-Hermitian bulk-boundary correspondence is established: the non-Bloch
winding numbers ($W_{0,\pi}$) characterize the edge states with quasienergies
$\epsilon=0, \pi$. In our non-Hermitian system, a novel phenomenon can emerge
that the robust edge states can appear even when the Floquet bands are
topological trivial with zero non-Bloch band invariant, which is defined in
terms of the non-Bloch effective Hamiltonian. We also show that the relation
between the non-Bloch winding numbers ($W_{0,\pi}$) and the non-Bloch band
invariant ($\mathcal{W}$): $\mathcal{W}= W_{0}- W_{\pi}$.
