  Upper critical field parallel to the conducting layer is studied in
anisotropic type-II superconductors on square lattices. We assume enough
separation of the adjacent layers, for which the orbital pair-breaking effect
is suppressed for exactly aligned parallel magnetic field. In particular, we
examine the temperature dependence of the critical field H_c(T) of the
superconductivity including the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF)
state, in which the Cooper pairs have non-zero center-of-mass momentum q. In
the system with the cylindrically symmetric Fermi-surface, it is known that
H_c(T) of the d-wave FFLO state exhibits a kink at a low temperature due to a
change of the direction of q in contrast to observations in organic
superconductors. It is shown that the kink disappears when the Fermi-surface is
anisotropic to some extent, since the direction of q is locked in an optimum
direction independent of the temperature.
