  Let $k$ be a commutative Noetherian ring. In this paper we consider filtered
modules of the category FI firstly introduced by Nagpal. We show that a
finitely generated FI-module $V$ is filtered if and only if its higher
homologies all vanish, and if and only if a certain homology vanishes. Using
this homological characterization, we characterize finitely generated
FI-modules $V$ whose projective dimension is finite, and describe an upper
bound for it. Furthermore, we give a new proof for the fact that $V$ induces a
finite complex of filtered modules, and use it as well as a result of Church
and Ellenberg to obtain another upper bound for homological degrees of $V$.
