  The three-chain Hubbard model for Ta$_2$NiSe$_5$ known as a candidate
material for the excitonic insulator is investigated over the wide range of
energy gap $D$ between the two-fold degenerate conduction bands and the
nondegenerate valence band including both semiconducting ($D>0$) and
semimetallic ($D<0$) cases. In the semimetallic case, the difference of the
band degeneracy inevitably causes the imbalance of each Fermi wavenumber,
resulting in a remarkable excitonic state characterized by the condensation of
excitons with finite center-of-mass momentum $q$, the so-called
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic state. With decreasing $D$
corresponding to increasing pressure, the obtained excitonic phase diagram
shows a crossover from BEC ($D\simg 0$) to BCS ($D\siml 0$) regime, and then
shows a distinct phase transition at a certain critical value $D_c(<0)$ from
the uniform ($q=0$) to the FFLO ($q\ne 0$) excitonic state, as expected to be
observed in Ta$_2$NiSe$_5$ under high pressure.
