  A non-complete geometric distance-regular graph is the point graph of a
partial geometry in which the set of lines is a set of Delsarte cliques. In
this paper, we prove that for fixed integer $m\geq 2$, there are only finitely
many non-geometric distance-regular graphs with smallest eigenvalue at least
$-m$, diameter at least three and intersection number $c_2 \geq 2$.
