We study the super-Grassmannian IGr n|n,s|t (C) formed by those graded subspaces of dimension s|t, s + t = n, of the vector superspace C n|n that are totally isotropic with respect to an odd skew-symmetric bilinear form b, defined in this superspace. We prove that IGr n|n,s|t (C) is a non-split supermanifold whenever t ≥ 1, s ≥ 2, and a rigid one whenever t ≥ 3, s ≥ 4. If t ≥ 2, s ≥ 3, then the Lie superalgebra of vector fields on this super-Grassmannian coincides with the simple classical Lie superalgebra πsp n|n (C) that annihilates the form b.