Let Gn,2n be the Grassmannian parameterizing the n-dimensional subspaces of C2n. The Picard group of Gn,2n is generated by a unique ample line bundle O(1). Let T be a maximal torus of SL(2n, C) which acts on Gn,2n and O(1). By [10, Theorem 3.10, p. 764], 2 is the minimal integer k such that O(k) descends to the GIT quotient. In this article, we prove that the GIT quotient of Gn,2n (n ≥ 3) by T with respect to O(2) = O(1)∅2 is not projectively normal when polarized with the descent of O(2).