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 ($Dsimg 0$) to BCS ($Dsiml 0$) regime, and then shows a distinct phase transition at a certain critical value $D_c(<0)$ from the uniform ($q=0$) to the FFLO ($q e 0$) excitonic state, as expected to be observed in Ta$_2$NiSe$_5$ under high pressure.
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