In this paper, we study the rigidity under Kähler deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case Grω(n, 2n + 1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.