  Let $V$ be an $n$-dimensional vector space over a finite field
$\mathbb{F}_q$. In this paper we describe the structure of maximal non-trivial
$t$-intersecting families of $k$-dimensional subspaces of $V$ with large size.
We also determine the non-trivial $t$-intersecting families with maximum size.
In the special case when $t=1$ our result gives rise to the well-known
Hilton-Milner Theorem for vector spaces.
