We discuss the 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 a fan representation and a quiver representation. I consider only quivers with canonical weight and we classify smooth such toric quiver varieties. I 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.

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