  We investigate the vortex state with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
modulations suggested for a high field phase of CeCoIn_5. On the basis of the
quasiclassical Eilenberger theory, we calculate the three dimensional structure
of pair potentials, internal magnetic fields, paramagnetic moments, and
electronic states, for the s-wave and the d-wave pairings comparatively. The
\pi-phase shift of the pair potential at the FFLO nodal plane or at the vortex
core induces sharp peak states in the local density of states, and enhances the
local paramagnetic moment. We also discuss the NMR spectrum and the neutron
scattering as methods to detect the FFLO structure.
