  The previously studied Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is
stabilized by a magnetic field via the Zeeman coupling in spin-singlet
superconductors. Here we suggest a novel route to achieve non-zero
center-of-mass momentum pairing states in superconductors with Fermi surface
nesting. We investigate two-dimensional superconductors under a uniform
external current, which leads to a finite pair-momentum of ${\bf q}_{e}$. We
find that an FFLO state with a spontaneous pair-momentum of ${\bf q}_{s}$ is
stabilized above a certain critical current which depends on the direction of
the external current. A finite ${\bf q}_s$ arises in order to make the total
pair-momentum of ${\bf q}_t(={\bf q}_s + {\bf q}_e)$ perpendicular to the
nesting vector, which lowers the free energy of the FFLO state, as compared to
the superconducting and normal states. We also suggest experimental signatures
of the FFLO state.
