Let ∇ be a symmetric connection on an n-dimensional manifold Mn and T*Mn its cotangent bundle. In this paper, firstly, we determine the fiber-preserving projective vector fields on T*Mn with respect to the Riemannian connection of the modified Riemannian extension ~g∇;C, where C is a symmetric (0; 2)- tensor field on Mn. Then we prove that, if (T*Mn; ~g∇;C) admits a non-affine fiber-preserving projective vector field, then Mn is locally flat, where ∇ is the Levi-Civita connection of a Riemannian metric g on Mn.
