Let G= SL(n, 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 G2,n. We prove that the GIT quotients of the Richardson varieties in the minimal dimensional Schubert variety admitting stable points in G2,n are projective spaces (see Proposition 3.5 and Proposition 3.6). Further, we prove that the GIT quotients of certain Richardson varieties in G2,n are projective toric varieties. Also, we prove that the GIT quotients of the Schubert varieties in G2,n have at most finite set of singular points. Further, we have computed the exact number of singular points of the GIT quotient of G2,n.