By changing the refractive index of a lens antenna from positive value to negative value, lens shapes are changed from the convex to the concave. A thick convex lens is replaced by a thin concave lens. In order to examine electromagnetic performances, electromagnetic simulations are effective. However, electromagnetic simulators useful for negative refractive index lens antennas are limited. In this paper, HFSS simulator is utilized. Amplitude distributions of electric fields in the near field region are obtained. Physical performances of the negative refractive index lens are clarified.