Based on transformation optics theory, an elliptical scattering-shifting cloak is designed and the constitutive parameter tensor expressions are derived. Then full-wave simulations to mimic the ellptical dielectric and conductor cylinder are obtained by using finite-element software. The results of full-wave simulations validate the constitutive parameter tensors we derived and verify that the scattering-shifting cloak can imitate any object including dielectric and conductor: these results provide a new theoretical approach to design cloaks.