  Pairing in an attractively interacting two-component Fermi gas in the absence
of the inversion symmetry and/or the time-reversal symmetry may give rise to
exotic superfluid states. Notable examples range from the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with a finite center-of-mass
momentum in a polarized Fermi gas, to the topological superfluid state in a
two-dimensional Fermi gas under Rashba spin-orbit coupling and an out-of-plane
Zeeman field. Here, we show that a topological FFLO state can be stabilized in
a two-dimensional Fermi gas with Rashba spin-orbit coupling and both in-plane
and out-of-plane Zeeman fields. We characterize the topological FFLO state by a
non-trivial Berry phase, and demonstrate the stability region of the state on
the zero-temperature phase diagram. Given its unique properties in both the
quasi-particle dispersion spectra and the momentum distribution, signatures of
the topological FFLO state can be detected using existing experimental
techniques.
