  Toric face rings is a generalization of the concepts of affine monoid rings
and Stanley-Reisner rings. We consider several properties which imply
Koszulness for toric face rings over a field $k$. Generalizing works of Laudal,
Sletsj\o{}e and Herzog et al., graded Betti numbers of $k$ over the toric face
rings are computed, and a characterization of Koszul toric face rings is
provided. We investigate a conjecture suggested by R\"{o}mer about the
sufficient condition for the Koszul property. The conjecture is inspired by
Fr\"{o}berg's theorem on the Koszulness of quadratic squarefree monomial
ideals. Finally, it is proved that initially Koszul toric face rings are affine
monoid rings.
