  In this paper, we consider the GIT quotients of Schubert varieties for the
action of a maximal torus. We describe the minuscule Schubert varieties for
which the semistable locus is contained in the smooth locus. As a consequence,
we study the smoothness of torus quotients of Schubert varieties in the
Grassmannian. We also prove that the torus quotient of any Schubert variety in
the homogeneous space $SL(n, \mathbb C)/P$ is projectively normal with respect
to the line bundle $\mathcal L_{\alpha_0}$ and the quotient space is a
projective space, where the line bundle $\mathcal L_{\alpha_0}$ and the
parabolic subgroup $P$ of $SL (n, \mathbb C)$ are associated to the highest
root $\alpha_0$.
