  For a symmetrizable GCM $C$ and its symmetrizer $D$, Geiss-Leclerc-Schr\"oer
[Invent. Math. 209 (2017)] has introduced a generalized preprojective algebra
$\Pi$ associated to $C$ and $D$, that contains a class of modules, called
locally free modules. We show that any basic support $\tau$-tilting
$\Pi$-module is locally free and gives a classification theorem of torsion-free
classes in $\operatorname{\mathbf{rep}}{\Pi}$ as the generalization of the work
of Mizuno [Math. Z. 277 (2014)].
