  We study smoothness of toric quiver varieties. When a quiver $Q$ is defined
with the identity dimension vector, the corresponding quiver variety is also a
toric variety. So it has both fan representation and quiver representation. We
work only on quivers with canonical weight and we classify smooth such toric
quiver varieties. We show that a variety corresponding to a quiver with the
identity dimension vector and the canonical weight is smooth if and only if it
is a product of projective spaces or their blowups.
