  Let $G=SL(n, \mathbb{C}),$ and $T$ be a maximal torus of $G,$ where $n$ is a
positive even integer. In this article, we study the GIT quotients of the
Schubert varieties in the Grassmannian $G_{2,n}.$ We prove that the GIT
quotients of the Richardson varieties in the minimal dimensional Schubert
variety admitting stable points in $G_{2,n}$ are projective spaces. Further, we
prove that the GIT quotients of certain Richardson varieties in $G_{2,n}$ are
projective toric varieties. Also, we prove that the GIT quotients of the
Schubert varieties in $G_{2,n}$ have at most finite set of singular points.
Further, we have computed the exact number of singular points of the GIT
quotient of $G_{2,n}.$
