Let Aq(Xn) be the quantum coordinate ring of the space of n by n anti-symmetric matrices.  Let g be a symmetric Kac-Moody algebra of type Dn and Uq(g) be the cooresponding quantum enveloping algebra. The main goal of this talk is to give the quantum cluster structure on Aq(Xn). We prove that the quantum cluster algebra structure on Aq(Xn) is isomorphic to the quantum cluster algebra AQ(q)(Xn)(Cw) arising  from a subcategory Cw of the module category of the preprojective algebra of type Dn with a Weyl group element w. Furthermore, as an application, we present a formula for PBW generators of the quantum unipotent subgroup of Uq(g).