The present invention relates to a metamaterial and a metamaterial antenna. The metamaterial is disposed in a propagation direction of the electromagnetic waves emitted from a radiation source. A line connecting the radiation source to a point on a first surface of the metamaterial and a line perpendicular to the metamaterial form an angle θ therebetween, which uniquely corresponds to a curved surface in the metamaterial. Each point on the curved surface to which the angle θ uniquely corresponds has a same refractive index. Refractive indices of the metamaterial decrease gradually as the angle θ increases. The electromagnetic waves propagating through the metamaterial exits in parallel from a second surface of the metamaterial. The refraction, diffraction and reflection at the abrupt transition points can be significantly reduced in the present disclosure and the problems caused by interferences are eased, which further improves performances of the metamaterial and the metamaterial antenna.