  We extend Calabi ansatz over K\"ahler-Einstein manifolds to Sasaki-Einstein
manifolds. As an application we prove the existence of a complete scalar-flat
K\"ahler metric on K\"ahler cone manifolds over Sasaki-Einstein manifolds. In
particular there exists a complete scalar-flat K\"ahler metric on the toric
K\"ahler cone manifold constructed from a toric diagram with a constant height.
