  We consider (iced) quiver with potential $(\bar{Q}(D), F(D), \bar{W}(D))$
associated to a Postnilov Diagram $D$ and prove the mutation of the quiver with
potential $(\bare{Q}(D), F(D), \bar{W}(D))$ is compatible with the geometric
exchange of the Postnikov diagram $D$. This ensures we may define a quiver with
potential for a Grassmannian cluster algebra. We show such quiver with
potential is always rigid (thus non-degenerate) and Jacobian-finite. And in
fact, it is the unique non-degenerate (thus unique rigid) quiver with potential
associated to the Grassmannian cluster algebra up to right-equivalence, by
using a general result of Gei\ss-Labardini-Schr\"oer. As an application, we
verify that the auto-equivalence group of the generalized cluster category
${\mathcal{C}}_{(Q, W)}$ is isomorphic to the cluster automorphism group of the
associated Grassmannian cluster algebra ${{\mathcal{A}}_{(Q, W)}}$ with trivial
coefficients.
