Electromagnetic external cloak is an important device, which can make an object outside its domain invisible, meanwhile the object can exchange information with the outer region. Based on line-transformation and the concept of complementary medium, an elliptical cylindrical external cloak with only axial parameter changed is designed in this paper. The expressions of material parameters are derived, and then the performance of the elliptical cylindrical external cloak is simulated using the full wave simulation software. The results obtained confirm the correctness of constitutive parameters tensor. In addition, the effects of loss on performation of external cloak are investigated. Finally, the distribution of constitutive tensors is also investigated. This work provide a feasible way to fabricate matematerial-assisted elliptical cylindcial external cloak.