In this short paper, we study $n$-representation-finite algebras from the
viewpoint of fractionally Calabi-Yau algebras. We shall show that all
$n$-representation-finite algebras are twisted fractionally Calabi-Yau. We also
show that twisted $\frac{n(\ell-1)}{\ell}$-Calabi-Yau algebras of global
dimension $n$ are $n$-representation-finite for any $\ell>0$. As an
application, we give a construction of $n$-representation-finite algebras using
the tensor product.