  We discuss the chiral phase diagram in the parameter space of lattice QCD
with minimal-doubling fermions, which can be seen as lattice fermions with
flavored chemical potential terms. We study strong-coupling lattice QCD with
the Karsten-Wilczek formulation, which has one relevant parameter $\mu_{3}$ as
well as gauge coupling and a mass parameter. We find a nontrivial chiral phase
structure with a second-order phase transition between chiral symmetric and
broken phases. To capture the whole structure of the phase diagram, we study
the related lattice Gross-Neveu model. The result indicates that the chiral
phase transition also exists in the weak-coupling region. From these results we
speculate on the $\mu_{3}$-$g^{2}$ chiral phase diagram in lattice QCD with
minimal-doubling fermions, and discuss their application to numerical
simulations.
