  We study superconducting phases in a quasi-two-dimensional multilayer system
without local inversion symmetry. Broken local inversion symmetry induces
layer-dependent Rashba-type spin-orbit couplings. We find that a complex-stripe
phase, which is the intermediate phase between the Fulde-Ferrell (FF) phase and
Larkin-Ovchinnikov (LO) phase, is realized in the magnetic field applied
parallel to the layers. A crossover from the FF phase to the LO phase appears
by tuning temperature and magnetic field. We show the local density of states
that characterizes the complex-stripe phase. As a possible realization of the
complex-stripe phase, we discuss the artificial superlattices of CeCoIn_5.
