  A partial flag variety is a smooth projective homogeneous variety admitting
an action of a maximal torus $T$. Schubert varieties are $T$-invariant
subvarieties of the partial flag varieties. We study toric Schubert varieties
in Grassmannian varieties with respect to the action of the torus $T$. Indeed,
we present an explicit description of the fan of a Gorenstein toric Schubert
variety in a Grassmannian, and we prove that any Gorenstein toric Schubert
variety in a Grassmannian variety is Fano.
