application of the overlap [@GW; @Neu] and domain-wall [@Kap; @FuSh] versions, both built on the Wilson-type kernel. Thus, in order to judge applicability of these new lattice fermions, it is essential to investigate the Aoki phase in the staggered-Wilson fermions. The phase structure for the staggered-Wilson fermion was first studied by using the Gross-Neveu model in Ref. [@CKM2; @MCKNO] and the present paper shows further investigation of this topic.

In this paper, we investigate strong-coupling lattice QCD [@KaS] with emphasis on parity-phase structure for two types of staggered-Wilson fermions [@Adams2; @Hoel]. Firstly we discuss discrete symmetries of staggered-Wilson fermions, and show that physical parity and charge conjugation can be defined in both cases while hypercubic symmetry depends on types of staggered-Wilson fermions. Secondly, we perform hopping-parameter expansion and effective potential analysis for meson fields in the strong-coupling limit. For this purpose, we develop a method to derive the effective potential for lattice fermions with multiple-hopping terms. The gap equations show that pion condensate becomes non-zero in some range of a mass parameter, which indicates that parity-broken phase appears in this range. We also study meson masses around the second-order phase boundary, and find that massless pions and PCAC relations are 