  The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state near the antiferromagnetic
quantum critical point (AFQCP) is investigated by analyzing the two dimensional
Hubbard model on the basis of the fluctuation exchange (FLEX) approximation.
The phase diagram against the magnetic field and temperature is compared with
that obtained in the BCS theory.
  We discuss the influences of the antiferromagnetic spin fluctuation through
the quasiparticle scattering, retardation effect, parity mixing and internal
magnetic field. It is shown that the FFLO state is stable in the vicinity of
AFQCP even though the quasiparticle scattering due to the spin fluctuation is
destructive to the FFLO state. The large positive slope dH_{FFLO}/dT and the
convex curvature (d^{2}H_{FFLO}/dT^{2} > 0) are obtained, where H_{FFLO} is the
critical magnetic field for the second order phase transition from the uniform
BCS state to the FFLO state. These results are consistent with the experimental
results in CeCoIn_5. The possible magnetic transition in the FFLO state is
examined.
