  Transition metal chalcogenide Ta$_2$NiSe$_5$, a promising material for the
excitonic insulator, is investigated on the basis of the quasi-one-dimensional
three-chain Hubbard model with two conduction ($c$) bands and one valence ($f$)
band. In the semimetallic case where only one of two $c$ bands and the $f$ band
cross the Fermi level, the transition from the $c$-$f$ compensated semimetal to
the uniform excitonic insulator takes place at low temperature as the same as
in the semiconducting case. On the other hand, when another $c$ band also
crosses the Fermi level, the system shows three types of
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic orders characterized by the
condensation of excitons with finite center-of-mass momentum $q$ corresponding
to the three types of nesting vectors between the imbalanced two $c$ and one
$f$ Fermi surfaces. The obtained FFLO states are metallic in contrast to the
excitonic insulator and are expected to be observed in semimetallic
Ta$_2$NiSe$_5$ under high pressure.
